I'm not aware of any rental facilities in the port itself but Hertz and Alamo are only about a mile from the entrance.
I took a limo from the Marriott Beach hotel to catch the Zuiderdam. If you are staying at a hotel nearby and only there for a night, a rental car might be a pain since you have to drop it off and still get a taxi to the port. If staying longer, I would go ahead and get the car. There is so much to see and do in Ft. Lauderdale.