Hi Amy,
Welcome back to the Disney Parks Moms Panel!
When my sons were younger, Disney Junior Play 'n Dine at Hollywood and Vine was one of our go-to dining spots for breakfast or lunch, but as they've gotten older their favorite characters have changed. There aren't any other options for either a character meal or table service breakfast at Disney's Hollywood Studios, but you could grab a quick morning bite at one of the counter service locations at park opening. Starring Rolls Cafe is one I'd recommend - it offers pastries, fresh fruit and soft drinks in the morning.
Another option for a character breakfast that's just a short boat ride away is the
Beach Club Breakfast Buffet at Cape May Cafe, where you can dine with Beach Goofy and Friends. Since Hollywood Studios opens at 9:00 a.m. on the date you'll be visiting, you might be able to get an early morning dining reservation that would get you to the park around the time they open the gates. When I just checked online for availability, there were still some 7:30 a.m. reservations available, so this might be a great alternative for your family.
I hope this helps with your vacation planning, Amy, and I know you'll have a magical trip. Please let us know if you have any other questions.
Beth