Also, even if you take it to an FFL, it may not be an "in and out" transaction- some localities require the dealer to hold it for a certain mandated period while the serial number is run to be certain it is not stolen, etc. This may be a state, county or city law or ordinance- check with the dealer first.
Also, check you dealer for the cost of this- dealers can be all over the map- some may charge $20 for this service, while another dealer up the street may want $100!
Let your fingers do the walking on the phone.