Hi Connie!
Welcome to the Disney Parks Moms Panel. The fastest (and least expensive) way to reach the rental car counter at the Walt Disney World Dolphin Resort would be to have a representative from the rental car company pick you up. If you are renting from Alamo, you can call them in advance to arrange a pick-up time. They will pick up guests within a five mile radius of their location. However, their rental car counter cannot pick you up prior to their office hours, which are currently 8 a.m. to 4 p.m. at the Walt Disney World Dolphin Resort location.
Of course, you could arrange for a private car service, Uber driver, taxi or
Minnie Van driver to take you directly from
Bay Lake Tower at Disney's Contemporary Resort to the rental counter. Those would be efficient, direct modes of transportation, too.
I had one additional suggestion. You may want to price out a rental car from the
Car Care Center at Walt Disney World Resort. It is much closer to Bay Lake Tower than the rental counter at the Walt Disney World Dolphin Resort and their counter opens two hours earlier so you could have the vehicle earlier in the day if you need it.
Wishing you many magical memories on your upcoming trip,
Jill