Hope you get this in time...
Yes, you can rent a car for a very reasonable price on Disney property. Last year, I rented a mini-van for transportation on the day of our arrival. For 7 of us, we were able to get to the Disney Property for $45 after taxes in a mini-van.
Disney has an
Alamo & National Car Rental desk at it's Car Care Center.
If you go to the Alamo.com website, you can put in your date and type in "ORLESS" in the Rate/Code Box. I put in Wednesday, May 25th and got these prices before taxes....
$19.99 Economy - Chevy Aveo
$21.99 Compact - Chevy Cavalier
$23.99 Midsize - Pontiac Grand Am
$28.99 Full Size - Chevy Impala
$49.99 Convertible - Chevy Sebring
$53.99 SUV - Chevy Trailblazer
....etc....
You can also rent at the airport and return on Disney property to the Car Care Center at no additional charge. That's what we did last year. We rented on our arrival day. Then, returned the car the next day. They have a shuttle that runs every 15-20 minutes from their office at the Car Care Center to the Ticket & Transportation Center where you can catch a monorail or a bus.
If you want to rent on a day after you have already arrived...you should call after arrival to set up transportation to the Car Care Center to actually rent the vehicle. I don't know if they tell you to go to the TTC and take the shuttle that I mentioned earlier or if they actually send a shuttle out to your hotel to get you.
On our departure day last year, we also rented a van from Alamo at the Car Care Center to get back to the airport. I called the day before and Alamo sent a shuttle bus to pick me up at a specific time at Pop Century and transport me directly to the Car Care Center for my rental.
Hope this helps...
Speed