Ceteris paribus -- and yes, I know that lots of other conditions would not remain the same, but this is just for fun -- Florida as an independent country would rank:
- 90th worldwide in land area at 65,755 square miles -- larger than, to name a few, Greece, Ireland, either of the Koreas, Tunisia or Cuba.
- 59th worldwide in population at 20.27 million -- more populous than, to name a few, Syria, Chile, the Netherlands, Somalia, Sweden or Portugal.
- 17th worldwide in GDP at $838 billion -- more than Turkey, Saudi Arabia, Egypt, the Philippines or Austria.
131 airports including seven hubs. 1,350 miles of coastline and six of the 100 largest seaports in the (current) US by cargo volume.
Maybe a little more reliant on tourism than would be comfortable for an independent country, but it's not the state's only asset. Florida is a major producer of citrus and sugar and provides 75% of the phosphates used for farming in the US (25% of the world supply).
Long after the Soviet Union's last gasp, Russia still launches its rockets into space out of Baikonur in Kazakhstan. I see no reason that Cape Canaveral shouldn't continue to provide launch services to e.g. NASA even if Florida goes its own way politically.
Independence looks plausible to me.