New York to Florida isn't a really long flight. I would not drug a dog if I did not have to. (Edie flies a lot and has never been drugged.)
The KEY is to get your pup used to the carrier. Take him all over town in it. Make it a safe haven and a fun place to be. If he feels safe in the carrier, I don't think you will have a problem.
Edie is always quiet when we travel UNLESS we see another dog in the airport. Then she goes crazy. it is embarrassing, but embarrassment has become a state of being for me since I became a Yorkie mama....