There is a National desk at the Dolphin. You could take your resort transportation to MGM and use the walkway to the Dolphin. We've dropped our car off late at night - you just hand it over to the valet.
Besides the Dolphin, there is also a National/Alamo rental desk at the Car Care Center. Complimentary shuttle service is availabe from (and back to) your resort. Ask about it at check in to arrange the pick up time. The Car Care Center has a bigger selection of cars than the Alamo and has longer hours of operation which may be more convenient.
We just rented a car for the day from the Dolphin as well. We even saw Jeb Bush there that day. I agree Cinderella37, it's pretty painless if you take a boat or walk from MGM. They are only open until 4 PM, keep that in mind .