IF you are staying at one of the WDW resorts, there are early morning busses to take guests to character breakfasts, tours, etc.
If it is not an EMH day at MGM, take the MGM bus and tell the driver you need to go to the Dolphin. It starts running (i.e. leaves the bus barn) about 7AM. Be at your resort's bus stop 45-50 minutes before you need to be at the Dolphin.
If it is an EMH day at MGM, take the bus to MGM, and then take the boat, or walk, to the Dolphin.