I think you need to budget a bit more than that. Cost of diy livery round here (Berkshire) is about £100-120 pcm and for that you get a stable and use of a field, but you are responsible for turning the horse out, bringing it in, and mucking out the stable. It can cost more or less than that depending on which part of the country you are in.
Other things you need to account for include shoes/foot trimming (£40-80 every 6-8 weeks,) feed/hay (how long is a piece of string? Depends on the quality of your grazing and the hard feed you give it,) bedding (£6-8 per bale/bag, usually one a week,) worming, teeth, insurance (at the very least public liability, you might want vet fees cover too or you might put the price of the premium in a savings account instead.)
I would also recommend lessons or Pony Club membership for your daughter too - many people overestimate the riding ability of their kids, and let’s face it we could all do with the odd lesson! Pony Club is about £70 a year and it gives public liability insurance as well as access to top level instructors that you wouldn’t be able to afford otherwise - my kids’ PC is doing a day at an Olympic rider’s yard this week.
Finally, I wouldn’t be buying a young 15hh horse for an 11 year old child. My 10 year old daughter is tall but slight for her age and she is just getting to know her new 14hh pony, who I expect will last her at least 2-3 years. It’s not a practical idea to buy a horse for your child to grow into - my own 15.2hh is fabulous but far too strong and forward for kids to ride. Also a young horse will need schooling by someone more knowledgable than the horse. Very few 11 yos have that skill and those that do will almost certainly come from a very horsey home. Far better to buy a pony that someone else has done the legwork with - a pony who can help teach your daughter is much more valuable to you than a young horse. Most kids want to get out there competing and having fun. Schooling a young horse takes time and patience that most kids don’t have. You can get some lovely connemaras, Welsh ds and new forest ponies out there that would be much more suitable for a child’s first pony, and natives are tough and live in fresh air so will cost less to keep.
Good luck - it’s hard work but exciting owning a pony and we wouldn’t be without ours (even if it does feel like we just throw all our money down a hole in the ground!) and the discipline needed to keep a pony fit, happy and healthy is good for kids, teaches them responsibility.