When you move to Florida, you have 30 days to change your driver's license. Make an appointment with your local License Center and try to make it on time with all the required documents. Here is a helpful site: http://www.dmvflorida.org/moving-to-florida.shtml
When I applied for FL license, they took away my NY's license. Later on a friend of mine told me that I could have kept my NY license if I told the DMV that I wanted to FL Driver's license only valid for FL. Check with your DMV if that's doable.
