The Plaza Inn has a character breakfast that you can make reservations for and eat there before the park opens. I believe you can also eat at the Carnation Cafe before the park opens as well without reservation.
As mom2rtk said, it's unlikely that you'd finish your meal before the park officially opens. If I recall correctly, the first ADR is from somewhere around 30 minutes before the park opens. If you do happen to finish before the park has opened, they'll hold you on Main Street with the rest of the pre-opening/rope drop crowds.