It depends where in state and how you want to live. In the Fairbanks area, $1k a month is pretty much the cheapest rent you'll find short of a dry cabin. Renting houses runs around $1500+utilities.
That said, a CDL with hazmat and a dual tank cert (don't know the proper name for it) will land you a job with pretty much all the overtime you can handle right now. Most places will start $15-20 depending on experience. IF you decide to come up, let me know and I can get you in touch with some folks. They are looking for a hazmat driver with double tank experience, and would probably pay a touch better and has crazy benefits.
On the other hand, with oil prices being so low the state is getting ready to take a huge hit and nobody knows what the effects will be. There are a lot, and I mean a lot of folks leaving AK right now.