Welcome, Anthony.
What a good father, to be looking into horses for your horse-crazy little one.
Instead of buying a horse for your daughter, I'd recommend lessons when she gets old enough (usually around 6 y/o).
Once she's had some lessons and her trainer can gauge her ability, the next step is to lease a horse or pony. Leases are usually kept on-farm, so your daughter will get the experience of taking care of a horse while being kept under a knowledgeable, watchful eye.
You don't have to ever
buy a horse, you know. Leases can and do last for years, and at the end of them, you give the horse back.
If you'd rather purchase a horse, then the riding instructor will be extremely helpful in finding you the right horse for your daughter. But this should only be done after your daughter has the ability and knowledge to ride correctly.
Good luck. Wish my father had cared that I loved horses!