Hi Kris2008! Welcome to Cruise Chat!
Its about a 40 mile drive from the airport to the Port. You don't want to attempt that in a taxi. You might be able to find a limo service that would do it, but I have never investigated that option.
We found renting a car (one way rental) to be the cheapest option if you have more than 2 people. You rent the car, drop it off at the rental office in Port Canaveral and they bus you to the port. They pick you up on the return end and you rent a car back to the airport.
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