I just recently sold one to a guy in Florida. Honestly unless I REALLLLLY want to sell what I have or trade for what is being offered, I never transfer from one FFL to another. You can do it either way. What you have to make sure of is to tell the buyer they have to pick an FFL that will accept shipment from a NON-FFL holder. it shouldnt be hard for them, and well if it is, and you dont want to spend the money to ship FFL to FFL then just wait for someone else to come along to make the buy.
When you mail it out, you really want to insure it, just incase something happens to the package and it gets lost, stolen or destroyed.
Package it VERY VERY well, LOTS of padding. Most of the time the word Fragile just means "kick harder" to the delivery guys.
I would include a photocopy of your license when you send the weapon. I have had times when it really wasnt necessary, and then there were times that I didnt send it and they were screwing over my buyer because they had no proof where the gun came from. Just end the drama before it starts, copy the ID and send it with the package. Nothing is more depressing than to pay for a gun, pay for shipping, wait 24 hours, only to get to the dealer and be told you cant have your toy *oh yeah, its 4:30pm on a Friday afternoon and they arent open on weekends* until the seller sends them a copy of their ID.