May I transport my firearms out of state when I move?

Yes. A person who lawfully possesses a firearm may transport or ship the firearm interstate when changing his or her State of residence.

Certain NFA firearms must have prior approval from the Bureau of ATF before they may be moved interstate. The person must notify the mover that firearms are being transported. He or she should also check State and local laws where relocating to ensure that movement of firearms into the new State does not violate any State law or local ordinance.

[18 U.S.C. 922(a)(4) and 922(e), 27 CFR 478.28 and 478.31]

http://www.atf.gov/firearms/faq/unlicensed-persons.html#gca-unlicensed-transfer