There is a good guide to this put out by the Australian Equine Veterinary Association and it should be read. We can send you a copy.
Some of my extra rules are:
The first cost is the cheapest.
Have you read all the needs and costs in keeping a horse?
Where are you going to keep it?
Are your fences safe?
Are you prepared to spend up to 10 times the cost of the horse on its gear soon after you get it? (Just think of the cost of a float)
If this is the first horse for your child then will it be totally safe (and that safety costs money and it should). Your child's life is worth more than a few hundred dollars in the price asked.
Don't forget that farriers are needed about once every 4 to 6 weeks if you don't develop the skills yourself. Average visit about $40.
Go along to the nearest Pony Club before you buy for at least three reasons. You don't have to own a horse to go along. You will be welcome. First, go because it's a greatworld-wide organization, well disciplined and structured. Second because there are always young people growing out of very good horses (kids get bigger) and you can get a hand me down from friendly people, one that is known and safe and... thirdly because you need to know quite a bit before you commit to any horse and pony clubs are training and fun groups. There are also some trail riding places around such as Highland Trails (Staverton) or other training establishments (Barry Lamprey, Sassafrass) (Bunjarra, Port Sorell). These people are mostly dedicated and will help you avoid errors. I haven't mentioned all and if any want to put links from this site then contact me.
Before you buy get a pre-purchase examination by an experienced equine vet first before delivery and NOT after your daughter has fallen in in love with it and won't hear anything said against it.
If it is a bit old and stiff in the joints it may be safer to learn on and it has probably been around pony club for a few years as well and knows the ropes.
As a parent of a horse loving child be prepared to have a pensioner around the paddock long after your child has grown, moved out, started a family and won't let you get rid of it.
There are a few more things to be said but it's in the AEVA book as well as in libraries everywhere.
Don't make the error of buying first and then wondering why your kid loses interest fast in an unplanned unpleasant premature and disorganized experience. You can't just point them in the direction of the horse and hope it will all work out. More time of the parents is spent on the job than is spent by the child. However, do it carefully, join a pony club first, borrow an old horse from a friendly member and it may well be a lifetime of rewards...and addiction.

