Any reason you are not just flying into Miami? A hotel in Miami near the port is not too expensive. Even if you stay near the airport and then taxi into the port the next day wouldn't be too bad. If you must go into Ft Lauderdale, do as Dave suggested and do the shuttle thing. By the time you paid to get back to the airport AND paid for the RCL transfer, you will have paid about 3 times (per person) what the shuttle will cost you.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013