You could find a smaller QH as well; then as they get bigger, they won't out grow it quite as quickly.
I had a shetland when I was a kid, and she was FABULOUS for a first time horse. But looking back on it, she didn't last me long, before I outgrew her...that's the biggest shortfall of ponies. If you can find a really well trained but smaller horse, that may be the better route, because you'll be able to keep it longer, and not have to 'upgrade' in a few years. I hated selling my pony after only having her for a couple years!
"The ideal horseman has the courage of a lion, the patience of a saint, and the hands of a woman..."