As far as the Feds and the Post Office are concerned, it's an antique and therefore isn't a firearm.
However (there's always a caveat) some local, State or City laws may say otherwise, so you need to know the rules from where it is going.
If you are shipping to an FFL holder you wouldn't need an FFL on your end, even if it was a modern rifle. The receiving FFL might want one though, it's up to him.
But, for an antique you probably don't need an FFL at either end. If there are no laws in the buyers state preventing it, you can send it straight to him.