Deborah,
If you visit either the Alamo or National Car Rental sites, you will find that you are able to rent a car from the MCO Airport in Orlando and drop it off at the Walt Disney World
Car Care Center. To my knowledge those are the only two operators that are available at that location. If you want to find out more information about
Car Rentals at the Car Care Center, you can see operating hours and other valuable shuttle information as well.
Make sure you check that out, as while there are convenient shuttle services available, they don't go everywhere all day long. This will help you plan out your rental!
On a personal note, I have also had success doing what you suggest with drop offs and pick ups at some of the resorts, like the
Walt Disney World Dolphin Hotel. I was staying there at the time, and it really made the exchange even more convenient.
Have a Magical Vacation!