Obviously the AR will have to be legal in the state that you're going to. If you're housed in barracks, you will have to keep it in the arms room. If you're housed in family housing, you can usually keep it in the housing, but it has to be registered with the Provost Marshall either way. I would go down there first, without the AR and scope out the situation. Then you can decide if it's worth bringing down after you find out what the regs are, the work schedule is, and the area's like. If there's no place to shoot it, it might not be worth bringing it. It's a PITA, as you will have to get the armorer to open the arms room to get your gun, and to put it back.
You will be considered a resident of that state if you have made a permanemt move (PCS). Generally speaking, if you're being paid TDY or any other temporary type pay, then it's not a PCS. If you're not, and it's a year long, then you're probably going to be considered permanent. It will really depend on what the orders say, and how they're written.
If it is a PCS, you can buy whatever the same as any other resident of the state. You'll need you're mil-ID and a copy of your orders to prove that you're a resident. If you're not permanent, then you can only buy the same as any other visitor to the state.
Ross