Actually, there are a couple of issues.
Out-of-state sales, requires that a FFL in the state of origin, packages and ships to an FFL in state of destination. Thus unless you are your self an FFL, under Federal law it is a crime to sell or transfer any firearm across state lines.
Only in-state can private party sells occur legally provide that both the seller and buyer are legally able to possess firearms in that state.
That said there are a host of legal issues for both the buyer and seller in private party sells.
For any number of reasons, I would consult a local gun shop and recommend that if you sell online, you use your local gun shop to transfer the gun for you.
You will usually pay the handling fee of your local FFL dealer (gun shop) and the buyer will handle the cost of the fee from the receiving FFL at the destination state. The reason I recommend this is dealers know the applicable federal and state laws dealing with firearm transfers. Because of possible criminal penalties, this is not an area of law where you want to make mistakes, knowingly or unknowingly. Ignorance is not a defense under the law.
Just, my $0.02. YMMV.