Check the DMV web site for the stateto which you may be moving. Also check the state website and/or the post office in that state to see if they have a new residents' guide.
When we moved to Nevada, we had a very short time in which to transfer the registration over for our cars and get new drivers' licenses otherwise we would have been find VERY heavily. Nevada also charged a special one-time fee when we registered our cars here (above and beyond therather high annualregistration fees which along with our high sales tax help the state 'make up' for our lack of state income tax.) Hopefully your state will be better but it's better to check with official sources rather than rely on hearsay from well-meaning people like me!