For your purposes, a DSLR would be great. The reason it's the best choice is the ability to shoot fast, to track moving subjects and the generally affordable flexibility of a DSLR system, which can easily be adapted for many difference purposes. You will also in most cases see a significant difference in image quality, coming from a point n shoot with a tiny sensor to an APS-C size sensor DSLR. The larger sensor also will allow you to use a considerably higher ISO, for lower light shooting.

But, how much do you want to spend?

I'll use some Canon examples below, just because that's what I use and am most familiar with. You have other choices... Canon and Nikon offer the most extensive systems, but other manufacturers might offer all you'll ever need.

To me, one ideal starter system for pet photography would be a Canon 70D with an EF-S 17-55/2.8 IS USM and EF 70-200/4L IS USM lenses. This is not cheap, but also isn't over-the-top expensive. This would be a roughly $3000 kit.

70D has a fairly advanced AF system... 19 points, all of which are faster/more accurate "cross type". It's also able to shoot 7 frames per second. For low angle shooting, it has an articulated LCD screen and a new method of Live View focus that's one of the quickest and most accurate from any manufacturer. This is a fairly advanced camera, but it has a lot of support for
first-time DSLR users, too. It uses a "true" pentaprism to give a larger,
brighter viewfinder, but at a little additional cost and weight... 70D currently
costs about $1100 from reputable stores.

The EF-S 17-55mm has f2.8 for low light and offers very high image quality. It has image stabilization and faster/more accurate/quieter USM auto focus drive. This would be your "walk-around" lens a lot of the time, useful indoors and short telephoto at 55mm for portraits, yet wide enough at 17mm for some scenics. This lens sells for about $880, and the separately sold lens hood for it goes for another $24. The 17-55mm is not sold in kits, but sometimes goes on sale (Canon Instant Rebates occur several times per year).

For more reach when chasing those puppies, the EF 70-200/4L IS USM will be a real workhorse of a lens, also with image stabilization and USM focus, as
well as covering a very useful telephoto range. I'm suggesting the f4 version
because it's about half the price of the f2.8 version. It's also about 1/3 smaller
and lighter. This lens sells for $1300 right now, including the matching lens
hood (with the f4 versions of Canon 70-200s, the tripod mounting ring is sold
separately for about $160). Also not sold in kits, but also usually included in
Canon Instant Rebate programs.

You might be able to get by with a single lens initially... the Canon EF-S 15-85mm IS USM is a top quality choice with both stabilization and USM focus drive ($900 + $24 for the separately sold hood). It doesn't have f2.8 aperture. But gives versatility with both wider and longer focal lengths in a single zoom, compared to the 17-55mm.

The 15-85mm also might pair up better for you with a longer telephoto such as the EF 100-400mm IS USM, if that were your choice... a 100-400 might be
better for wildlife, birds... and okay for pets... but a bigger, heavier, and more
expensive lens ($1700, incl. hood and tripod mounting ring).

Lower cost Canon camera alternatives:

Rebel T5i/700D instead of 70D... The $700 T5i has a bit more support for first time DSLR users, but is a little slower to shoot with, 5 fps (instead of 7 fps), and slightly different control layout. Also 1/4000 top shutter speed (vs 1/8000 on 70D), 1/200 flash sync (vs 1/250 on 70D).

T5i also has less sophisticated AF system.... 9 points (vs 19 on 70D and 7D, 65 on 7D Mark II), although all 9 points are the "better" cross type. T5i has two focus patterns: All Points and Single Point (vs three on 70D: All Pts, Single Pt, and Zone.... vs five on 7D: All Pts, Single Pt, Spot Single Pt, zone and Expansion... vs seven on 7D Mark II: All Pts, Single Pt, Spot Single Pt, Coarse Zone, Fine Zone, 4-Pt Expansion, 8-Pt Expansion. T5i has articulated LCD screen and Live View, but it's LV focus method is an older type that's considerably slower.

Rebel T3i/600D... Similar to T5i, except less expensive at $550 (with basic 18-55mm kit lens), it uses a simpler 9-point AF system with only the single, center point the "better" cross type. And not quite 4 frames per second shooting speed.

The Rebel SL1 is an especially small and lightweight DSLR. Functionally it's very similar to T3i, except it's LCD screen is not articulated. It sells with 18-55mm kit lens for about $50 more than T3i. There are also T5 and T3, which are the most entry level Rebel models (T5 is fairly new and likely will replace the T3 in the line-up).

I am not recommending the 7D or 7D Mark II for someone buying their first DSLR... both these are aimed at fairly experienced users and have less support for beginners. The now-five-year-old 7D is selling out at very good prices, and can be better than 70D in some ways for action photography, but is relatively older model now. 7D Mark II sounds like quite a nice upgrade, but is going to be considerably more expensive than 70D when it comes available later in October.

Lower cost Canon lens alternatives:

Often you can buy lenses in kit with the camera for some savings. There are manufacturer assembled kits (i.e., Canon put lens & camera together)... and there are retailer assembled kits. In general, the manufacturer assembled kits are pretty good. Some of the retailer are, too... but some are not and you have to be very careful about what's being included in the kit.
With Canon cameras you will find several Canon lenses bundled in kits, which are also available separately at lower cost than the more advanced lenses mentioned above...

EF-S 18-55mm IS "Mark II" is the most common and least expensive kit lens. It's decent optically (a lot better than the earlier versions), but has rather pokey and noisy micro motor focus drive. If bought separately, it sells for about $200 (plus $25 for the lens hood).

EF-S 18-55mm IS STM is a step up that's about $50 more expensive and has
smoother, quieter, maybe a little faster and more accurate "Stepper Motor" auto focus. It's especially good for videography. For still photography, the USM (Ultrasonic) focus drive found on the more advanced lenses is better yet, especially for action photography because it's the fastest and can be the most accurate.

EF-S 18-135mm IS is a significant step up from the 18-55, both in build quality and in focal length range, that costs about $500 bought separately. It's another micro motor lens, and there is also an STM version that sells for about $50 more.
The 18-55mm are more likely to be offered in bundles with the Rebel/xxxD series cameras. The 18-135mm is more likely to be offered bundled with the more advanced 60D, 70D series and 7D series cameras.

EF-S 55-250mm IS is sometimes found as a kit lens in two-lens bundles. It's got surprisingly good image quality for a $250 lens (when purchased separately). And, yes, there is a $50 more expensive STM version of this lens, too. All around, it's a fine lens.

An older design EF 75-300mm is sometimes found offered as a second lens in two-lens bundles... It's one of Canon's least successful lenses and I'd suggest avoiding it. Not to be confused with several much better, but more expensive EF 70-300s (and certainly not the premium 70-200s)... the 75-300 can be found selling separately for $200 and less.

All these micro motor and STM focus drive lenses will not be as good tracking and keeping up with active subjects, compared to the more premium USM
lenses mentioned above. STM will be better than micro motor. And STM is the top choice for video (so long as it's paired with a camera that can take advantage of it). But for still photos of moving subjects, USM is better than STM.

I'm sure if you look at Nikon, Olympus, Pentax, Sony, etc. you will find similar choices.

If you decide on Canon, one way to stretch your budget a bit further can be with refurbished cameras and lenses at the Canon Online Store. These are










often demos or just returned overstock, sometimes have little or no real use.. You'll often see a spike in what's offered right after a trade-show, and it's a pretty good bet they are selling off what was shown and used there. Higher end gear is sometimes returns from the Canon Professional Network lender system, right after major events (i.e., the Super Bowl), where Canon shows up with a truckload of gear in support of the pros shooting the event. Of course, sometimes it's returned items and might be repaired.

But, Canon's refurbs now typically carry the same warranty as new and they have a liberal return/exchange policy, if unhappy with what you receive. Some of the major online retailers also occasionally have refurbs to sell (Adorama and B&H Photo, for example). Or, check out their used equipment
departments, for some savings. Of course, many folks simply prefer brand
new. And that's fine, too.

There are also third party lenses (and other accessories) that might help you stretch your budget a bit. The "big three" are Sigma, Tamron and Tokina... and they offer some good lenses. I prefer OEM when possible... I figure Canon is the best at optimizing their lens performance on their cameras. Third party manufacturers have to reverse-engineer things, while avoiding patent infringements, making their job a bit more difficult. But 3rd party stuff can be attractively priced... and might do the job very well... and sometimes even
offers things the OEM system doesn't. So it's worth considering.

Thank you to every one who has given me a response good or bad it is really helpful i have been meaning to go to a camera store to try out the cameras and see how they feel in my hands but just haven't had the time and for the people who are wondering what camera i have now it is the canon PowerShot SX160 IS and it is a fantastic camera i have loved it for 2 years now but sometimes it just isn't fast enough to capture the picture i have captured many fantastic pictures of my dog with it but if it doesn't capture it fast enough then i wind up with a blurry could be fantastic picture and this happens about 30 present of the time

Thank you to every one who has given me a response good or bad it is really helpful i have been meaning to go to a camera store to try out the cameras and see how they feel in my hands but just haven't had the time and for the people who are wondering what camera i have now it is the canon PowerShot SX160 IS and it is a fantastic camera i have loved it for 2 years now but sometimes it just isn't fast enough to capture the picture i have captured many fantastic pictures of my dog with it but if it doesn't capture it fast enough then i wind up with a blurry could be fantastic picture and this happens about 30 present of the time