Seems like this sort of question comes up regularly. Being an FFL has forced me to research these laws, so even though this is more than what you asked for I'm going to give a more complete reply in hopes of answering future questions:
Dealers licensed in this state (FFL):
Non-Licensed residents of this State:
- Can sell longguns to residents of any State, provided the purchaser is at least 18 years of age and all provisions of the Brady law are met.
- Can sell handguns to residents of this State only, provided purchaser is at least 21 years of age, the laws of both States are complied with, and all provisions of the Brady law are met.
- Can sell firearms to any FFL (regardless of State of residence).
Non-Licensed residents from another State:
- Can buy longguns or handguns from FFLs licensed in this State, provided all provisions of the Brady law are met.
- Can sell personal firearms to any FFL.
- Can buy and sell personal firearms to non-licensed residents of this State only (just be sure you're not "engaged in the business of dealing in firearms" without an FFL--exact qualifying criteria left unspecified by ATF so good luck knowing when you hit the magic limit )
- Cannot buy from or sell to non-licensed residents of any other State.
- Cannot ship in interstate commerce, except to themselves or an FFL, a firearm that has otherwise been lawfully aquired; must, when shipping to themselves, declare the firearm to the commercial or contract carrier.
- Can sell firearms to any FFL.
- Can buy longguns only from FFLs licensed in the State, provided the laws of both States are complied with and all provisions of the Brady law are met.
- Can order firearms from any FFL and have them shipped to an FFL in their State of residence in accordance with State and Federal law.
- Cannot buy handguns.
- Cannot buy or sell firearms to non-licensed individuals.
Note that substituting 'acquire' for 'buy' and 'dispose of' for 'sell' in the above would be more proper (since it may not be a sale). I wrote it up this way for readability.
So, final answer for your specific case is: "It depends on if you are trying to buy a longgun (yes) or handgun (no)".
Hope this helps!