I might read more from this website and a few other websites before deciding it's okay, but.....
I googled "can you carry a gun in your auto all 50 states"
It appears okay to lock up an unloaded gun while traveling. If you think you are unsafe where you plan to stop at night, look up specifics for that state either beforehand or when you get there as to whether you can load your gun while there at night. Personally, I would probably just load it at night whether it was allowed or not, as it's better to be alive and safe and in trouble over it rather than be dead.
I got this answer at "http://www.secondcalldefense.org/self-defense-news/traveling-your-gun-legally"
For the most part, Federal law is pretty straightforward. No federal permit is required. And the Firearms Owners' Protection Act (FOPA) shields you from local restrictions if you're transporting firearms for lawful purposes.
Under FOPA, notwithstanding any state or local law, a person is entitled to transport a firearm from any place where he or she may lawfully possess and carry such firearm to any other place where he or she may lawfully possess and carry it, if the firearm is unloaded and locked out of reach. In vehicles without a trunk, the unloaded firearm must be in a locked container other than the glove compartment or console. Ammunition that is either locked out of reach in the trunk or in a locked container other than the glove compartment or console is also covered.
Exceptions apply to those who are convicted felons; persons under indictment for felonies; adjudicated "mental defectives" or those who have been involuntarily committed to mental institutions; illegal drug users; illegal aliens and most nonimmigrant aliens; dishonorably discharged veterans; those who have renounced their U.S. citizenship; fugitives from justice; persons convicted of misdemeanor crimes of domestic violence; and persons subject to domestic violence restraining orders.