Nonliberal is correct in that it is illegal for a Non-licensed individual to ship a handgun via the USPS postal system. Long guns are ok but handguns are a big no-no.
You can ship it to another state resident via UPS or FedEx. UPS or FedEx will require it to be shipped overnight which is going...
Here is a write up I did on the process a while back. Not to sound negative but, it's not as much fun as you think. You really have to love what you do.
http://www.theoutdoorstrader.com/threads/187582-So-you-want-to-get-a-FFL