Wow, beautiful shape!
Original refrigerator should have been a Dometic RM 2300 series gas/electric. Chances of finding a working authentic one are pretty slim, but I suppose you could if you searched hard enough. Not that it would be easier, but you could look for a broken one and rebuild/replace the cooling unit part of it instead.
The hard part would be to get a panel and a cabinet door handle for it to put on the face of the refrigerator that would match your interior. I always tell people to save that panel if they get rid of the original refrigerator.
The good news is, it's a woodgrain and not a wallpaper.
2007 T-286SR Cherry/Granola, #6236, original owner, current mileage: 9467.8 (as of 5/26/19)
1997 T-2653 Blue Denim, #5471
1979 12 1/2' MC, Beige & Avocado, #4639
Past Sunlines: '97 T-2653 #5089, '94 T-2251, '86 T-1550, '94 T-2363, '98 T-270SR