Make sure the inverter is large enough to handle the inrush current of the fridge compressor at start up. I tried a 600w inverter, initially. It would not handle the large inrush current. I now use a Xantrex Prowatt 1000w and it is silent and handles the load easily.
If you want automatic transfer for the inverter and the fridge only, there are single circuit transfer switches available.That is an easy installation. If you want whole house transfer for powering other circuits, you'll need a transfer switch capable of that whole house load, typically 30 amps with a travel trailer.
You'll get more specific advice by listing your RV, the model of fridge you are going to use, and the components of your 12V system.