Hi, Jenny! The schedule changes frequently, and there may be times when there are no morning shows. I checked the schedule for this week, however, and I do see shows beginning as early as 10:30, so there are morning shows available, depending on the day.
You can see an approximate time schedule by visiting
Hollywood Studios Disney Junior Live. You'll see the schedule of shows for today, and a small calendar icon next to it that you can click on to check upcoming show times. Take the show times with a grain of salt - the times guide is changed weekly, and you are likely to see future times changing. This, however, may give you some idea of what you can expect.
I really hope you have a fantastic time! I can't wait to see the new show myself. Don't tell my kids, but I even tune in to see Doc and Sofia when they're at school!