What are you going to do when you are not driving? Do you want to be restricted to campgrounds with electrical hookups? Are you planning on stopping along the way for sight seeing, eating in a restaurant or any other activity?
I think the dorm refridge idea needs to be rethought. You have a couple of better choices. First you could replace the refridge with a new unit. Or you could replace the worn out components.
If you want to go with an electric unit, then I recommend getting a suitable 12v system which will use much, much less power than a dorm 120v unit. If you go that route, you should also consider solar power and a decent battery bank.