My car has IL plates, ...words...words....
Each state has their own rules. I had to do some fine print reading and make a few phone calls to figure it all out (plus they threatened to revoke my driver's license).
I went through the same thing with AZ. They required a form to be filled out and signed by the local police department indicating that they "saw the vehicle in their jurisdiction" or something like that.
Be sure to double check the state that you move to. TX has some interesting rules about bringing a vehicle into the state, but provides exemptions for military members. Google is great way to find DOT websites....