I believe, in general, that a shotgun would be less problematic than a handgun, and if you're using it for wilderness protection, it may work for you.
Keep in mind that in some states if you get pulled over, you must immediately disclose that you have a firearm to the police. And, I know that in the state of Maryland, you must carry your firearm unloaded with the ammo in a separate compartment of the vehicle. Not sure if there is an exception for a concealed carry permit or if Florida's would be considered acceptable in MD, but it's nearly impossible to get a CC permit in Maryland.
Also, you are not getting into any sensitive sites like the White House or other museums in DC with any kind of weapon if you're planning on visiting them or other cultural sites.
In general, the north does not take kindly to weapons, especially handguns, and they are highly regulated. I would research every single state before you travel through it.