Just returned yesterday from an Eastern Caribbean cruise onboard the Carnival Liberty.
Flew in to Miami Airport the day before. A couple of tips ..... depending on where your hotel is (if you go in the day before) you really don't need a rental car. Take a taxi. It's cheaper. However, we rented a car (we didn't know) and had to return it back to the airport Saturday.
Since Miami is such a large cruise terminal Carnival has a couple of things to help you. Technically you can check it at the airport for your cruise (they will take your luggage and you can pay for transportation to the port). Your second option is to check in at the cruise terminal.
Loved 8356. 8356 is the Port side of the ship (left side). You can literally see the sunrise every morning from that side. There are 2 days you can't (those are the days you are on your way back). You can't hear the noise from lido. It's wonderful!!