Directly at the entrance of the port FLL there is a office from THRIFTY together with DOLLAR ( Miami Road) . So you have the choice to take the car at the airport, drive to your pre- cruise hotel and give the car back at the port. From there you can take the free shuttle which takes you directly to your ship. Tip: go on their web and take the blue member card for free , so when you check in with this card you spare time.
This is a photo from the shuttle at pear 21:
This is Thrifty at Miami Road above you see the Port Entrance: