I'd probably go for a pony, but not a tiny one. Maybe around 13ish hands? At that height they'd still be pretty manageable, not now for her, but soon. If it's not too fine an adult should be able to occasionally ride it if required. It would hopefully give her maybe 5 - 6 years at least before she outgrows it.
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.