I see heaps of children around 8 years old, but sometimes younger, and they bring their parents quiet stock horses to pony club, often 15 - 16 hands high. Lovely horses and all but the kids constantly need help saddling, bridling, rugging etc.
I think when she's a bit older your daughter might want to have a horse that is small enough so that she can care for it, and saddle and bridle it herself, yet big enough so she doesn't outgrow it in a few years.
I'm 22 now and my horse isn't big, maybe 14.2ish. I love the slightly smaller height, so much easier to do stuff with I find.