The airport is a 10 minute drive from the pier. Assuming your flight comes in on time - you will be fine. We always fly in the day before so that we don't worry about our flights.
You most likely will be off the ship by 9:30 or 10:00. You often can get off as early as 8:00.
After you disembark, go to the airport and check your luggage in, take a cab to Las Olas Blvd. which is gorgeous and has loads of places to explore, wonderful restaurants, etc. Just make sure you get back to the airport in time to catch your flight.
Can't do this any more. At Ft Lauderdale airport they will not accept your luggage for check in more than 4 hours before the flight. Just last month, we saw an awful lot of people with later flights just sitting around the main ticket areas by the windows
and around the "edges" of the terminal sitting on their luggage and waiting for the 4 hour check in window to begin.