The running joke about MD is that they don't recognize ANY State's permits--not even their own in some cases.
Unfortunately it is not a joke...
Your FL permit isn't worth the plastic it's printed on in MD. The MD State Police have testified in their General Assembly that they oppose reciprocity with ANY state because they believe that the investigative procedures and capabilites of LEAs in other states are so substandard and untrustworthy that there is no way that MD can trust that the people with permits issued by other states would meet MD's "stict requirements".
Funny thing about that is MD is one of the only states in the Union that has no classroom training or range qualification for the issuance of their License. That and the fact that the MSP, and the LEAs in the urban 4 counties of MD have some of the highest numbers of Federal Civil Rights violations ruled against them of ANY LEAs in the nation, and MD LEAs have paid out TENS of MILIONS of dollars in Federal Civil Rights damages to citizens in the last decade.
But the police in OTHER states are the untrustworthy and incompetent ones, in their eyes...
Anyway, the only way to legally transport a firearm through MD is under FOPA rules. You need to unload the gun, store the ammo in a separate container, and have the gun in a place inaccessible to the driver or passengers.
In the trunk is good if you're in a car.
If you have an SUV (I have a Chevy HHR, so this is how I do it) put it in the very back of the vehicle.
I have an MTM ammo box with a padlock for my ammo and mags (you DO NOT have to unload the mags, just take them out of the gun), and I put my firearms in locked boxes, which are tethered to the tie-down rings in the back of my HHR with Kyptonite bike cables.
I also have printouts of the FOPA code that I put in my gun safes--ON TOP of the guns, and a printout of the MD Attorney General's ruling on loaded mags being legal to transport, that I put in the ammo box--ON TOP of the mags.
Also, you need to know that to remain compliant with FOPA conditions (and NOT come under Md statutes) you need to be driving straight through--not stopping for the night, or shopping at Ikea, or sightseeing or whatever. The only stops you can make under FOPA are "incidental stops" like for fuel, or meals, or bathroom breaks at a rest stop.
Make sure your lights on your vehicle are all in order. Make sure your tags are in order. Make sure you obey the traffic laws, and for heaven's sake, DON'T speed. Out-of-state plates are like bear-bait in the People's Republic of Maryland, and they LOVE pulling over out-of-staters and handing out pieces of "paying paper", because they know that travelers RARELY will show up for the court date to contest traffic citations.
Follow the rules, keep your eyes open, and don't drive like an a$$hat. Maryland is a pretty small state, and if you're driving through on I-95, it's only an hour or two that you need to be concerned with.
Once you "cross the moat" into VA, you're ollie-ollie-oxen free...