Based on my carnival cruise a couple of weeks ago, if everything from disembarkation went smoothly expect to be be let through security at 10:30am to be seated, 11:00 checkin begins, 11:30 boarding the ship was the official procedure. We were actually about about 10mins ahead of schedule on each portion. Boat was empty for at least the first hour, very nice to explore without the first day crowds.
I also recommend the dig at atlantis if you like aquariums it's very large so give yourself 2 hours to go through. They have a manta ray that's 11 feet across and it's a baby!