You can, by Florida law, carry a firearm on or about your person without a concealed-carry license provided it is "unloaded and in a secure wrapper", and is being carried "from a place of purchase to the home" or "to or from a place of repair."
A "secure wrapper" isn't defined in the law, but is accepted as a closed bag (such as a gun bag/case) or the box meant for it.
To eliminate unnecessary drama, I'd make the "secure wrapper" look like something else, such as a guitar case or beach umbrella bag. Make sure you have the dated bill of sale with you as well.
EDIT: I just reviewed the relevant statute, and it appears to pertain only to a "pistol." Further research regarding a long gun, I guess, is needed. I'll see what I can find. All I can find for now is to leave the gun shop directly en route to a lawful hunting, fishing, or camping activity, or a lawful shooting activity, participate in such activity, then proceed directly home from such activity. Possession of a firearm without a concealed-carry license is lawful during these activities, or while in transit directly to or from these activities.
If the store has a range, the lawful shooting activity can take place there.
I think it would be easier to offer a few bucks to someone from the store to drive you home with it.