Have a look at the Firearms Owners Protection Act, specifically the "Safe Passage Provision".
http://en.wikipedia.org/wiki/FOPA
Basically, provided that the ownership of said gun is legal at both her starting and ending point, she's going to have to keep the gun unloaded and "not easily accessible" while on her trip.
If she stops overnight at a hotel or whatever, she may keep the pistol loaded with her in her room, provided that it
stays in the room. If she goes out for ice, or to ask for more towels at the front desk, she must leave it behind in the room.
And as CoRoMo mentioned, certain states (such as IL and NY) don't exactly agree with the FOPA provisions, and they WILL give her the business if she is pulled over and the gun is found. Your best bet is to avoid such areas to begin with, but if they must be driven through, be very, very good and do not give them a reason to pull you over.