Absolutly, I have sold a few guns to some of my friends.
Though like a used car you sell, it is a good idea to write up a Bill of sale. As a seller, you cannot sell to someone who you know is prohibited from purchasing a firearm. (if you know they would be denied a purchase in the store, you should not sell to them as it is probably illegal)
There is no paperwork to file with the Gov for a private purchase. In fact even if you wanted to "register" the gun, Georgia Law prohibits it.