There's a whole section of this forum devoted to growing hops. There's a lot of good knowledge there, and there are plenty of books on the subject if you're serious about growing them.
The hop rhizomes that you buy are pretty much just root cuttings, so I imagine if you dug up the plant in the fall and took a main section of the root network with you, they would be transportable. That being said, they typically don't produce hops in the first (or even second) years, so you'd have to let the plant establish itself again before getting any kind of usable yield at the new place. It may just be better to wait and buy the rhizomes after your move.