As far as I know, there is a waiting period in all of Florida. Most counties are three days, but Palm Beach is 5 working days.
To answer your question, yes, you can buy a gun anywhere in Florida, since you are a resident.
My suggestion, if you do not want to wait, is to get your CCW. It will take at least 90 days to get it after the class, but makes it easier to purchase a firearm.