Just go to the guest relations deck and ask for the early luggage tags. You should be off the ship 8am. You shouldn't have a problem, I've made it to the Ft. Lauderdale airport from the Port of Miami by 10am more than once. It's only 15 minutes from Port Everglades to the airport.
If you do early departure, this means that you have to carry ALL of your luggage off. I did this when I cruised back in October of 2007. However, this was when we docked in Miami at 7:00 am and I had a noon flight out of Miami, which is only about 10 minutes from the port. If you decide to do this, you should be off the ship within 15-30 minutes of it docking, (Royal Caribbean frequent cruisers disembark first, I think they are referred to as Diamond members), then self departure.
One thing though. If you do early departure, you cannot have more than two bags including your carry on per person.
2007 - Majesty of the Seas (Bahamas)
2009 - Enchantment of the Seas (Western Caribbean)
2010 - Freedom of the Seas (Western Caribbean)
2013 - Golden Princess (Alaska, roundtrip from Seattle)
Why would you want to get off the ship before the first color code is announced? You'll have plenty of time to get to the airport, you could even have breakfast before you leave. 1 1/2 hours before your flight is plenty of time to arrive at the airport. I hate sitting in airport any longer than I have to.
I agree with Sonny. Self-debarkation is not as wonderful as it sounds. It has become too popular, and in my opinion abused, and thus not a quick exit from the ship. How fast is something that half the passengers decide to do? I frankly wish the cruise lines would stop it and return to the old ways, which when properly implemented were quicker.