You can rent a car at the Dolphin from National or Alamo. There are also several rental companies at the hotels near DTD. We've rented from National and picked up at the airport and dropped off at the Dolphin and vice versa. We've also done this at the Courtyard with Dollar. It's a short walk from DTD. Here's a list I saved from a post I read sometime ago:
WDW Car Rental
National- Car Care Center
Walt Disney World Dolphin
Alamo- Car Care Center
Walt Disney World Dolphin
Dollar- Courtyard by Marriott
Hotel Plaza Blvd.
Lake Buena Vista, FL Avis- Hilton
1751 Hotel Plaza Blvd.
Lake Buena Vista, FL Budget- Doubletree Hotel
2305 Hotel Plaza Blvd.
Lake Buena Vista, FL
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