I know it is legal for an 18 year old to own, sell, and buy a handgun through a private purchase, but can i ship a gun to an FFL dealer coming from a private seller?
Your question is a bit confusing. So, I will answer it both ways:
1. Yes, you may ship a gun (long arm or handgun) to an FFL. Perfectly legal. Check with the FFL first, though, to make sure they will accept shipments from private parties (their company policy, not law).
2. Can you receive a gun from an FFL that you bought from a private party at 18? Long guns, yes. Handguns, no.
