daboss: Unless you need a car in Miami, there's a shuttle from Lauderdale airport to the Miami Airport....it used to be called "Super Shuttle" and was about $15.00. You could then get a cab to the Port. You could call Lauderdale Airport Ground Transportation Dept. and they will tell you. There might even be a shuttle to the Port of Miami. Driving can be nerve wracking, especially I-95, so if you don't need a car in Miami, I'd investigate letting someone else worry about it.
We used tri-county transporation to get from FLL to Miami. www.floridalimo.com
They have several options depending on the number of people you have. They will take you to the pier or anywhere in Miami if you are going a day early.