There are SEVERAL rental car places near the port...In our situation we are arriving a day before. Once we fly into Orlando we are renting a car and driving to Port Canaveral and staying at the Four Points (Sheraton) for one night (near port), then we are waking up (breakfast) returning our car to the rental place (1min from the port) and the rental shuttle will be taking us to the port. We are doing the same thing going back...Shuttle will pick us at @ port, then take us to get our car and we drive back to Orlando, drop car off and take shuttle to terminal. It's the easiest way for us. If we do a transfer it'll be about the same $. We figure that we rent a car for our own timing issues (we are adamant about being on time). Its' better than waiting for loads of people to board a shuttle which can take up to and sometime over an hour.
So yes, there are several rental car places within 1 - 3 minutes from the port. If you rent a car you can take it near the port to the rental place / more than likely there will be a fee.