*not a lawyer
Legally there is probably no law directly stopping you from mailing it within your state. There is a law that states you must meet all of the policies of whatever carrier you are using. Every carrier has a policy that they won't ship firearms to an individual. So, in conclusion, you can not legally mail it to someone in state unless you can find a carrier who will mail it in state.
Lots of people just don't tell what it is, but this is against the law.
I would go through an FFL anyways as you have absolutely no idea who is on the other end of the transaction. Could be a 12 year old kid.
You usually don't have to mail from an FFL legally from your side, but some states require an FFL receive from an FFL, so in that case you have to in order for the FFL on the other end to accept the shipment.
It is a real pain and I avoid shipping absolutely whenever I can.