"high quality MGP"? Does this mean high build quality? High image quality? High megapixel count?

"small full frame" is sort of counterintuitive. Small camera, large sensor is not something you find together. A large sensor needs a larger camera.

"great telephoto fixed lens" Telephoto lens is a long focal length. Smaller cameras with powerful telephoto capability accomplish that feat by having very small sensors... the opposite of "full frame". A "fixed lens" is a lens that has only one focal length... such as "300mm". It is not a zoom lens. I am guessing you simply mean a non-interchangeable lens, that you would consider a zoom. Many compact cameras have zoom lenses for the versatility. Especially those with telephoto capabilities. The smaller number that have fixed a fixed lens use a "normal" or "slightly wide" lens, not a "telephoto".

"For travel"... Well, that can be pretty much anything. I've traveled with a full frame DSLR fitted with a battery grip, 20mm, 24-70mm, 135mm and 300mm lenses, as well as a flash, 1.4X teleconverter (for use on the 135mm and 300mm lenses), macro extension tubes, lens and sensor cleaning kit, light meter, spare batteries, charger, extra memory and more. I've also traveled with a small APS-C mirrorless camera, four small prime lenses (12mm, 22mm, 56mm and 90mm), macro tubes, lens adapter, macro tubes, spare battery/charger, extra memory and a few other things... with a total weight less than the full frame camera/grip alone! Some people take a "bridge camera" or a "point n shoot" (both use non-interchangeable zoom lenses) that makes for an even lighter and more compact kit.

Full frame point-n-shoots:
Here are eight non-interchangeable lens cameras that have full frame sensors offering between 37MP and 47MP resolution... three are Leica, four are Sony and one is a Zeiss camera. https://www.bhphotovideo.com/c/products/Point-Shoot-Digital-Cameras/ci/8612/N/4288586279?filters=fct_sensor-size_3087%3Afull-frame All of these cameras are fitted with a fixed focal length, moderately wide lens (28mm or 35mm). None offer telephoto.

APS-C point-n-shoots:
The next size smaller sensor is APS-C and there are only eight of these available too, with resolutions between 24MP and 29MP. Four are Ricoh, Fujifilm offers two models, while Canon and Sigma each offer one. As with the above cameras, most of these have a fixed, non-interchangeable, moderate to slightly wide (28mm to 40mm full frame equivalent) lens. The Canon has a modest zoom that's equivalent to 24mm wide angle to 72mm short telephoto. https://www.bhphotovideo.com/c/products/Point-Shoot-Digital-Cameras/ci/8612/N/4288586279?filters=fct_cameras-kits_7135%3Acameras-only%2Cfct_sensor-size_3087%3Aaps-c The smaller sensor used in these cameras will make for a bit less low light shooting capability, more noise issues at higher ISOs.

Micro 4/3 point-n-shoots:
Next we have so-called Micro Four-Thirds (M4/3) sensors... a little smaller still. Currently only three cameras use this sensor format, two Panasonic and one Leica, all of which are 17MP. All three also have similar zoom lenses, equivalent to full frame 24mm wide angle to 75mm short telephoto. https://www.bhphotovideo.com/c/products/Point-Shoot-Digital-Cameras/ci/8612/N/4288586279?filters=fct_cameras-kits_7135%3Acameras-only%2Cfct_sensor-size_3087%3Afour-thirds

1" point-n-shoots:
You'll find a much larger selection among so-called 1" (one inch) sensor format cameras. Twenty four models use this next size smaller after M4/3 and their resolution ranges from 15MP to 23MP. Sony and Panasonic each offer eight 1" cameras, Canon offers five, Ricoh two and Leica one. https://www.bhphotovideo.com/c/products/Point-Shoot-Digital-Cameras/ci/8612/N/4288586279?filters=fct_cameras-kits_7135%3Acameras-only%2Cfct_sensor-size_3087%3A1in Several have fixed focal length, moderately wide lenses... but twenty one offer a zoom. Many of those zooms are modest, but others have fairly powerful telephoto "reach", equivalent to full frame 200mm, 400mm or even 600mm! Several of these are what are known as "bridge" cameras, similar in appearance to DSLRs, except that their zoom lens is not interchangeable.https://www.bhphotovideo.com/c/products/Point-Shoot-Digital-Cameras/ci/8612/N/4288586279?filters=fct_cameras-kits_7135%3Acameras-only%2Cfct_sensor-size_3087%3A1in%2Cfct_telephoto-35mm-equiv_4088%3A200mm%7C250mm%7C360mm%7C400mm%7C480mm%7C600mm

1/2.3", 1/2", 1/5" point-n-shoots:
There are many "point n shoots" that use these even smaller format sensors, some of which have truly extreme telephoto range... equivalent to full frame 800mm, 900mm, 1000mm, 2000mm and even 3000mm! In other cases the tiny sensors used in these allow for the most compact cameras, but all these smaller sensor cameras are much more susceptible to digital noise, which significantly limits how high ISO can be used as well as limiting shooting in lower light conditions. Resolution is also limited by sensor size, typically between 12MP and 20MP. https://www.bhphotovideo.com/c/products/Point-Shoot-Digital-Cameras/ci/8612/N/4288586279?filters=fct_cameras-kits_7135%3Acameras-only%2Cfct_sensor-size_3087%3A1-2.3in%7C1-2.0in%7C1-5in

I hope I'm on the right track with this and that it helps you find what you want. If you wish, you can further refine the searches at B&H Photo to narrow it down to a smaller selection. Once you've identified a few, do further research on them and look for good, detailed reviews.

"high quality MGP"? Does this mean high build quality? High image quality? High megapixel count?

"small full frame" is sort of counterintuitive. Small camera, large sensor is not something you find together. A large sensor needs a larger camera.

"great telephoto fixed lens" Telephoto lens is a long focal length. Smaller cameras with powerful telephoto capability accomplish that feat by having very small sensors... the opposite of "full frame". A "fixed lens" is a lens that has only one focal length... such as "300mm". It is not a zoom lens. I am guessing you simply mean a non-interchangeable lens, that you would consider a zoom. Many compact cameras have zoom lenses for the versatility. Especially those with telephoto capabilities. The smaller number that have fixed a fixed lens use a "normal" or "slightly wide" lens, not a "telephoto".

"For travel"... Well, that can be pretty much anything. I've traveled with a full frame DSLR fitted with a battery grip, 20mm, 24-70mm, 135mm and 300mm lenses, as well as a flash, 1.4X teleconverter (for use on the 135mm and 300mm lenses), macro extension tubes, lens and sensor cleaning kit, light meter, spare batteries, charger, extra memory and more. I've also traveled with a small APS-C mirrorless camera, four small prime lenses (12mm, 22mm, 56mm and 90mm), macro tubes, lens adapter, macro tubes, spare battery/charger, extra memory and a few other things... with a total weight less than the full frame camera/grip alone! Some people take a "bridge camera" or a "point n shoot" (both use non-interchangeable zoom lenses) that makes for an even lighter and more compact kit.

Full frame point-n-shoots:
Here are eight non-interchangeable lens cameras that have full frame sensors offering between 37MP and 47MP resolution... three are Leica, four are Sony and one is a Zeiss camera. https://www.bhphotovideo.com/c/products/Point-Shoot-Digital-Cameras/ci/8612/N/4288586279?filters=fct_sensor-size_3087%3Afull-frame All of these cameras are fitted with a fixed focal length, moderately wide lens (28mm or 35mm). None offer telephoto.

APS-C point-n-shoots:
The next size smaller sensor is APS-C and there are only eight of these available too, with resolutions between 24MP and 29MP. Four are Ricoh, Fujifilm offers two models, while Canon and Sigma each offer one. As with the above cameras, most of these have a fixed, non-interchangeable, moderate to slightly wide (28mm to 40mm full frame equivalent) lens. The Canon has a modest zoom that's equivalent to 24mm wide angle to 72mm short telephoto. https://www.bhphotovideo.com/c/products/Point-Shoot-Digital-Cameras/ci/8612/N/4288586279?filters=fct_cameras-kits_7135%3Acameras-only%2Cfct_sensor-size_3087%3Aaps-c The smaller sensor used in these cameras will make for a bit less low light shooting capability, more noise issues at higher ISOs.

Micro 4/3 point-n-shoots:
Next we have so-called Micro Four-Thirds (M4/3) sensors... a little smaller still. Currently only three cameras use this sensor format, two Panasonic and one Leica, all of which are 17MP. All three also have similar zoom lenses, equivalent to full frame 24mm wide angle to 75mm short telephoto. https://www.bhphotovideo.com/c/products/Point-Shoot-Digital-Cameras/ci/8612/N/4288586279?filters=fct_cameras-kits_7135%3Acameras-only%2Cfct_sensor-size_3087%3Afour-thirds

1" point-n-shoots:
You'll find a much larger selection among so-called 1" (one inch) sensor format cameras. Twenty four models use this next size smaller after M4/3 and their resolution ranges from 15MP to 23MP. Sony and Panasonic each offer eight 1" cameras, Canon offers five, Ricoh two and Leica one. https://www.bhphotovideo.com/c/products/Point-Shoot-Digital-Cameras/ci/8612/N/4288586279?filters=fct_cameras-kits_7135%3Acameras-only%2Cfct_sensor-size_3087%3A1in Several have fixed focal length, moderately wide lenses... but twenty one offer a zoom. Many of those zooms are modest, but others have fairly powerful telephoto "reach", equivalent to full frame 200mm, 400mm or even 600mm! Several of these are what are known as "bridge" cameras, similar in appearance to DSLRs, except that their zoom lens is not interchangeable.https://www.bhphotovideo.com/c/products/Point-Shoot-Digital-Cameras/ci/8612/N/4288586279?filters=fct_cameras-kits_7135%3Acameras-only%2Cfct_sensor-size_3087%3A1in%2Cfct_telephoto-35mm-equiv_4088%3A200mm%7C250mm%7C360mm%7C400mm%7C480mm%7C600mm

1/2.3", 1/2", 1/5" point-n-shoots:
There are many "point n shoots" that use these even smaller format sensors, some of which have truly extreme telephoto range... equivalent to full frame 800mm, 900mm, 1000mm, 2000mm and even 3000mm! In other cases the tiny sensors used in these allow for the most compact cameras, but all these smaller sensor cameras are much more susceptible to digital noise, which significantly limits how high ISO can be used as well as limiting shooting in lower light conditions. Resolution is also limited by sensor size, typically between 12MP and 20MP. https://www.bhphotovideo.com/c/products/Point-Shoot-Digital-Cameras/ci/8612/N/4288586279?filters=fct_cameras-kits_7135%3Acameras-only%2Cfct_sensor-size_3087%3A1-2.3in%7C1-2.0in%7C1-5in

I hope I'm on the right track with this and that it helps you find what you want. If you wish, you can further refine the searches at B&H Photo to narrow it down to a smaller selection. Once you've identified a few, do further research on them and look for good, detailed reviews.