It is about 45 min-1 hr from Orlando to Port Canaveral ( all depending on the traffic, which is usually bad around Orlando) You would be going a long way out of your way to go that route. A taxi would be a fortune. Check with the car rental agency to see if they have an office at or near the port in some of the hotels.
Not meaning to be nosy, but could you possibly drive your own car down and back? Parking is $70.00 for the week but thats cheaper than a rental and it's painless parking right at the dock.