From The Truth About Guns:

Interstate transport of firearms in the US is not heavily regulated, and there are protections in place for legal owners to move their weapons across state lines for legal purposes.

The inadequately respected Second Amendment is the foundation of your right to travel with firearms. More clearly, 18 U.S. Code § 926A: ‘Interstate transportation of firearms’ protects someone passing through even states which would not otherwise allow you to possess them, so long as your possession is legal in your destination. (Some states like New Jersey are extremely strict even about meal stops so it is best to plan no stops there at all.)