You can book through Alamo (if you are a Costco member they have a discount through the Costco.com website) and choose the "Walt Disney World Car Care Center" as your p/u and d/o location. They have a shuttle to/from the resorts.
National is now owned by Alamo so you can rent one through them too the same way (but no Costco discount). The Dolphin resort also has a desk & cars onsite but since you are staying at the GF the car care center would be more convenient.