I think its illegal in FL, but I don't think its a severe fine, no more expensive or time consuming than paying for the tag an getting it over with. You might have a 30 day grace in Florida, I remember being told that but when I googled it a long time ago I could only find reference to vehicles, not trailers. < sorry
Side note: I was told (3rd hand) That no tag is better than a borrowed tag, I had a guy tell me that his friend was pulled over with a tag from a different trailer and the cop told him that he was "being nice" by suggesting that he remove the tag immediately (while the cop did paperwork) and accept the ticket for no registration with no complaints, option B was that he was going to have the trailer towed to an impound lot and he gets a 2nd degree misdemeanor.
< not sure of the accuracy but that story motivated me to never swap tags over to a new purchase ever again, now I just tow it home with my fingers crossed and the bill of sale in my pocket. I think i've towed home un-tagged trailers about 15 times if not more over the past few years and eventually my luck will run out.