We did the same thing....got a little dorm fridge, and also used a cooler.
Check to see if your fridge is covered by any recall. I had a new cooling unit installed for free! I did have to pay for a new circuit board, since that wasn't part of the recall.
Go to the mfgr's site to see if your unit is covered.
I had the little dorm fridge held onto the galley table with a ratchet-type cargo strap:) It worked great! And you start to figure what you really need to have refrigerated, because of the limited space.
Happy Cammping:)