The monorail does run early.
I think that they early breakfasts are probably not that early that you would be done much before the park really opens. Cinderealla's Table starts at 8am, and the park opens at 9am - so I would think that you wouldn't be done that much before 9am!
I have not experienced a character breakfast in MK before opening (we will on 4/22), but at EPCOT, they had the Worldshow Case roped off right after Norway prior to it opening at 11am - they had CMs standing there as well. Future World opens at 9:00, so the same as MK, I would not think you would really be done in less than an hour.