No, but a national law already exists, the one we used for 150+ years until after the Civil War when licensing and other racist gun laws were started to keep freed slaves from owning firearms. That would be the 2A...but getting BACK to that standard will take action, action that is occurring at the state and national levels, refer to Heller and McDonald, and see the loosening chains around many of the states. You'r own Florida led the charge in 1985, IIRC, with the first Shall-Issue CCW permit I just got my AZ CCW permit...took about 5 minutes to do the application and send in the money order, and then about 7 weeks for it to come back. Used to be about 5 days, but they cut the staff by half and permit applications are going up drastically. I just had to show previous training - 10 years in the law enforcement field didn't hurt, but my antique permit that expired in 1998 did the trick.
There is only one state that doesn't have a permitting system in place, and that's Vermont, which has has lawful permitless CCW for over 200 years.
I think you are on the right track but wrong answer. Yes, we should utilize the Full Faith and Credit provision to recognize the right to carry a concealed firearm in all 50 states, and just like a drivers license, the fed doesn't get to state the rules. See, the feds don't make the driving rules, each state does, which is why it's legal to make a right on red some places, others it will get you a ticket. Montana for a while didn't have a highway speed limit, while some places still say 55MPH shall be the law.
While we get SCOTUS to hammer out what 2A means, (for those in government who can't read all 27 words), I agree, we should use state reciprocity to lead the way, which means Vermont's DL would be their CCW permit.
A new federal law gives the fed.gov another foot to put in the door to stamping out CCW where they find it, and many of them up there dream of that. I would not give them that extra opportunity.