There is a Playhouse Disney character breakfast and lunch at MGM Studios that has 2 of the Little Einsteins characters as well as JoJo and Goliath. I haven't been to it but have heard great things about it for little ones.
Also - I believe the restaurants are open when they have Extra Magic Hours, they may even open before regular park time on other days. I would check with the reservation people when you make your ADR's for the earliest breakfast time available.