I have read horror stories and I don't think I will ever arrive late at the ship. Plan on getting to the ship as close to noon as possible so that you can enjoy the sail away party.
We had the unfortunate experience this trip of forgetting a suitcase in Miami after we arrived at Fort Lauderdale airport (traveling with a three-year old can make you crazy at times). To make a long story short, I got back to Miami to claim my suitcase at the office there and return in plenty of time for my return flight. There were some sad faces in Carnival's office when I got there which could mean a) oh no I forgot my passport and/or license; b) on no my luggage is lost; c) (from the cruise that just disembarked) someone took my suitcase; d) on no I didn't fill out the online forms properly for my fun pass - this could be more than a nightmare if you read cruisemates regularly. People do not realize how necessary it is to have that Fun Pass in hand when you arrive for your cruise! It takes just a few minutes to fill out the online forms.
Don't arrive late in case there's a problem. If you arrive late, Carnival doesn't have time to help resolve the problem.