You do not need to re-register a legally owned handgun in NC unless you want a concealed carry permit.
As far as transportation, each state has their own regulations as to what is legal or illegal, but generally, you should be fine as long as the firearm is unloaded and inaccessible to the vehicle occupants while in the act of interstate travel.
State Laws -
http://www.nraila.org/GunLaws/
Interstate Transportation of Firearms
The following is a citizen's guide to legal transportation of personally-owned firearms for hunting, competitive shooting, vacationing, and changing residence between states. This guide does not cover the lawful carriage of concealed firearms.
http://www.nraila.org/GunLaws/Federal/Read.aspx?id=59