Private Party Firearm Sale - Virginia

I responded to a want ad on Armslist.com for a S&W 910 pistol, which I happen to own. The buyer is located in Florida and wants to know if his niece can pick up the pistol for him (she lives in Virginia). I told him that for that to happen, I would need to meet her at a local FFL dealer to complete the transaction. Is this the legitimate way to go about the sale? Something tells me it isn't lawful to release a firearm to someone knowing it is intended for someone else that I know nothing about. If I wrote up a bill of sale with his niece's name, address, etc. on it as if she was purchasing it, would that be okay, or is it better to do it through a dealer so a background check can be performed?