Again referring to the dying Constitution, even if there wasn't a Right To Bear Arms, you should have no problem carrying your weapon into other states as long as you have a permit in one state:
Article IV
Section 1. Full faith and credit shall be given in each state to the public acts, records, and judicial proceedings of every other state. And the Congress may by general laws prescribe the manner in which such acts, records, and proceedings shall be proved, and the effect thereof.