Wow, Fort Lauderdale to Port Canaveral is a good distance. The Equinox will be on schedule. There is a car rental at the airport which is only about 10 minutes from Port Everglades. This might be a good way to get to Port Canaveral. I don't know of any shuttle service that would be "reasonable". This
company may be able to give you a price. Check with the car rental companies as well, we have Alamo, Hertz, Avis, Budget, Enterprise to name a few, which I'm sure you have some of these in Germany.
Sounds like a busy vacation ahead for you. Best Wishes!