First of all, yes, if you rent a car in FL you will need an infant seat. No exceptions. (As others have stated hiring a limo/cab has different rules).
Almost all of the car rental companies DO rent car seats around here, however it typically runs $9-12 per day and you never know what you're getting. Given the length of your trip, you may be better served (since you don't have to rush straight to the ship) to have one driver get the car, drive <3 miles to the WalMart near MCO and pick up a cheap car seat that you can either dispose of once you're done with it, or just check for the trip home. Airlines are required to check car seats for free anyhow.
Are you renting the car for the duration of the cruise, or turning it in and getting a new rental for your return trip to MCO? If you're parking the car, just leave the seat there for the duration of the cruise. If you're turning it in and doing a second return rental, call the Port Canaveral car rental office (not the national answering/booking service) and see if it would be possible for you to store the seat there while on your cruise, or call your disney vacation planner and see if they have any way to store an infant seat for the duration of the cruise.
My own personal preference though (from LOTS of traveling) - I got a device called a Brica Roll N Go when I was travelling with my infant son a lot. It was a lifesaver. It was $70 and it strapped onto the back of my infant seat allowing it to cart seat & child through airports with ease, and then folded up flat. It's not really functional as a stroller (not enough ground clearance for the great outdoors) but it will get you around an airport/cruise terminal letting your child ride in the comfort of it's own car seat. Both can be gate checked at the plane (free of charge). I took a small umbrella stroller when I was cruising with my son, but he rode through security at the cruise terminal in his car seat/roll-n-go combo and then I was able to have my car seat with me on the ship and we could take cabs without me being a panicky mom.