What you CAN do though is use a VIRGINIA based FFL holder (gun shop) that will receive the pistol from you & they, (the FFL) will legally transfer to the buyer if the buyer can pass the NICS check in VA.
Here is how:
Gun has to get to the VA FFL. You can use a "common carrier" including Brown (united postal service) or Fed Ex. Policies vary and they require overnight service from a main shipping center (ie no Mail Boxes Inc.).
This part is key: YOU MUST INFORM THE CARRIER THAT YOU ARE SHIPPING A HANDGUN (a u of md basketball star was recently convicted of failing to tell FedEx of the guns in packages he shipped.)
NOW, there might be another way: once your buyer finds an FFL/gunshop in VA, ask the gun shop if you can drive down and deliver the gun you own to THE GUN SHOP. Only the gunshop can take possession of the gun - NOT the buyer. You are allowed to visit VA with a gun - everyone knows that. And you are allowed to transfer your gun to an FFL holder in any state (that's what you are doing when you FedEx to an FFL holder) - everyone knows that too.
AFAIK, there is no law that says that the "common carrier" can't just be you. Why take chances with FedEx stealing "loosing" your gun? Seems safer to just drive to the VA gunshop and transfer to the FFL.
Again, check with the VA gunshop first.