Talk to the dealer you intend to buy from and see what he wants as far as residency proof. I also live in 2 states and used my property deed and two utility bills as proof of residency in my second state. Soon thereafter I acquired a state issued ID card for the second state, and that works like a charm with any dealer.
Federal law says you are a resident of a state whenever you are residing in that state. If you move from state #1 to state #2 and the next day what to purrchase a firearm, you're good. There's no minimum time requirement. All you need to do is provide proof of residency in the second state.