OC in VA is not dependent on being a resident, so you are fine in that aspect. One thing to keep in mind is that there is federal property scattered all over the Northern Virginia area right outside of D.C., so you need to have a good map and do some research before you travel too far from wherever you are staying.
Also, I found this regarding the airport.
Reagan National is physically located in Virginia but has a Washington, D.C. mailing address. Where is the Airport located legally?
Ronald Reagan Washington National Airport is located in Virginia. Federal law and Virginia Code both state the Airport is "situated within the Commonwealth of Virginia" (see 59 Stat. 552 (1945); 1950 Va. Code Sec 7.1-10 (1983)). There are also court decisions holding the airport is located in Virginia (see Pfister v. Director, Office of Workers Compensation, etc., 675 F.2d 1314, 1315-16 (D.C. Cir. 1982); and Bryan v. District of Columbia Unemployment Compensation Board, 342 A.2d 45 (D.C. Ct. App. 1975)).
When the federal government operated Reagan National and Dulles prior to 1987, both Airports had Washington, D.C. postal addresses. Tocontinue identifying the service area more easily for travelers, the Authority did not change the addresses.
So, it appears that you just have to deal with the standard airline and TSA rules for checking firearms.