As said word of mouth is the best way, just like finding a permission. Get some lessons under her belt & a bit of experience.
There are plenty of ponies out there that have been outgrown that owners want someone trustworthy to ride, often for nothing.
Best way to find out about these is through pony club or from somebody who already goes, most of the ponies have been passed round the kids as they grow and are well known by the parents, if you do decide to buy one at a later date it takes most of he guesswork out of getting a good one.
My eldest daughter started when she was five and she absolutely loves it. I'd much rather she was out in the countryside, keeping fit & active enjoying life rather than being stuck in front of the telly!
Don't be put off,
ATB,
Rich