Disney runs special early morning buses for the various breakfasts all around WDW. The MK service begins around 6:30am daily and the the rest of the World service starts around 7am. Just be at your resort bus stop around 45 minutes prior to your reservation. The buses don't run too often that early and this will allow you extra time if you just miss one.
There is a turnstile open at every park for diners to enter before the park opens to the public. The Cast Member will check your name on their dining list. Make sure you bring your dining reservation number along just in case they can't find your name.
ps....DO NOT take any transportation info from anyone other that the purple pants people at WDW.....the Disney bus drivers. For whatever reason most Cast Member on the phone or at your resort will give you bad info. If you are not sure.....ask here or a bus driver.
Welcome to the DIS!