The Independence of the Seas is normally scheduled to arrive back in port at 5:30am. However, it still has to clear customs and normally the earliest they allow passengers to disembark is around 7:00 - 7:30. If, and that's a big if, you can be one of the very first ones off the ship, there is a remote possibility that you can get to the airport by 8:00am. And since you're required to be there at least an hour before departure, it might work.
But the possibility is so slim, that I would not suggest trying it and I usually don't suggest scheduling a flight before noon, just to be on the safe side.
If you have no choice, then I would talk to the Purser's Office when you get on the ship and let them know you have to be the first off the ship. You'll have to keep your luggage and take everything with you.
Keep in mind that the only way to get from the pier in Ft. Lauderdale to the Miami airport in this situation is going to be by taxi and the price will be $75 plus tip.