Long Hunter--You will need a hunting license ($85) a moose license ($500) and a harvest permit (free). Depending on what area you want to hunt you will either need to apply for the lottery in Nov 2011 (I think) to hunt 2012 or you can purchase a tag over the counter for some of the general hunt areas. Do you know where what area you want to hunt yet, or if you are using a guide?
Last year a guy was transporting moose to the lower 48 for people with a refrigerated semi. I'm not sure if he will be doing it again or how much he charged, but it would be something to look into.