Could you find a yard, even one a bit less local where your DD would have a chance to learn some stable management? I used to work at a yard that would have children for the day from 8, so there may be somewhere that's local enough for her to go at least once a fortnight/once a month to gain some skills before you commit to buying.
As a small adult, I used to to a lot of exercising of children's ponies and the one bit of advice I would absolutely give you, is not to overhorse your daughter. Buy the pony she needs at 12 (or whatever age you choose to buy at) not the one you think she will want in a few years time. This is probably the quickest way to kill a child's confidence in a lot of cases. Also, this is one reason why loaning a first pony can be a good idea.
At 12, a child can do most of a pony's day to day care, if they're a nice pony and a reasonable size for the child (and the child is competent), however, there are lots of things I don't think they should be responsible for:
-Turning out, catching in. IMO, this should always be done with adult supervision, especially if there are other horses in the field.
-Feeding hard feed. Unfortunately, mistakes when feeding can make a pony very ill, or even be fatal, so it's not something that I would make a young teenager responsible for, just in case.
-Making any kind of decision about veterinary care, or attempting first aid. I'd want someone to always be on site and willing to help with any injury or illness. Realistically, you're probably going to be the one who makes the decisions about when to call the vet, what to vaccinate for, when to have teeth done etc, obviously with some advice from someone knowledgeable where possible.
-Any decisions about shoeing, again, you'd probably have to be the one to make decisions about this.
-Checking the fit of tack. Most ponies will change shape at various stages of their lives, and it's important someone is keeping an eye on this. Hopefully your instructor would point out anything glaringly wrong. This goes double for choosing what tack to use- she can't buy a grackle just because it looks cool, or put on exercise bandages without knowing how to do this properly, or decide she suddenly wants to ride bitless.
-Leading or riding on roads alone. Unfortunately, this is unavoidable at many yards, but I wouldn't want her doing it alone just in case something went wrong. In general, hopefully hacking alone can be avoided.
-Anything like clipping or pulling the mane without being shown how and being sure the pony is safe (even if nothing bad happens, it will lead to the poor pony looking awful!).
There are probably other things that I can't think of right now, but basically you would need an adult on site at all times, who, crucially, would be willing to take change of the pony in the event of an emergency.
You're also probably going to be expected to be the one to make decisions about certain things- on a basic level, things like shoeing and vaccination, but also more serious veterinary care decisions. You might also be expected to decide what to feed, and maybe whether it's time to buy a new saddle or rug. Some yard owners and vets will be willing to help and advise more than others, though.
I do think working livery could be a good solution for you, if you manage to get an agreement that works for you. However, working livery brings a lot of its own problems, and sometimes you need someone on your side with more horsey experience to see where these problems might be. Also, it won't suit every pony, so you would need a back up plan in the event of things not working out.
Good Luck, whatever you decide. If it helps, my parents made a decision very early on that they would never buy me a pony. Riding is still one of my "things" and I have always found ways to ride if I've wanted to.