Just make sure you comply with all TSA and airline rules.
I don't know where you are coming from, if you have a concealed carry permit from that state, if you intend to carry concealed, etc.So all I can say to you is if you carry openly, you should have no problem.
Permits to carry are not required in Virginia to open carry a pistol/revolver. Ensure you do not place it in a console or glove box of your car, it would be concealed then. Leave it on your hip or on the passenger seat, you should be okay.