There are places nearer than the airport. On WDW property, there's the car care center near MK. Either the Swan/Dolphin has a car rental desk. I believe a few of the DD hotels have car rental desks at their locations. My suggestion would be to check with an agency you're considering and call them, asking for their locations. Some agencies will bring a car to you or you to them.
It may be a good idea to rent from an agency which is in terminal at the airport, then you don't waste time with shuttles when you drop it off.
Wish I could be more specific for you. Perhaps you should post this question on the Transportation board.
HTH!