We just came back from WDW and we ran into the same question. We had a non-park day and wanted to go to DS for breakfast. Most of the places have brunch (Sundays only) and require reservations. Also, some had "Walk-up" unavailability.
Without reservations, there is Earl of Sandwich --- only one that does true breakfast besides the bakery / donut show
With reservations, you have:
Raglan Roads (brunch)
Chef Art Smith's (brunch)
Wine Bar George (brunch)
City Works (brunch)
STK Steakhouse (brunch)