There is lots to think about when buying a pony, even though it's very exciting. Do bear in mind that a 9 year old who has ridden roughly once a week for 2 years on safe, riding school ponies is no way comparable in experience to a 9 year old who has ridden ponies a lot from an early age! She really is just a novice, so it's important that anything you buy her is safe, sane and easy to do.
At 9, some of the things I'd be thinking about would be-
-What will happen when she outgrows the pony? At 9, with a safe first pony type, this is very likely to happen, probably within the next 4-5 years max, so it is something you would have to plan for. There are lots of options available of course, but it is something worth thinking about, especially if you cannot afford to keep two ponies.
-What would you do if the pony became lame, injuried or otherwise unable to work for a long period? Could you also afford to pay for her to have lessons if this happened?
-What about things like going on holiday as a family? Who would look after the pony then? There are obviously lots of solutions to this problem, but it is something to think about.
-What happens if she loses interest?
Also, it is worth thinking about worst case scenarios. Even hardy native types are relatively expensive to keep, as well as the aditional costs of replacing tack and your daughter's equiptment as she grows. It would be good to think about what might happen if you/your husband ever lost your jobs or needed to move e.g. to be closer to family.
I'm not saying this to put you off getting a pony, but these are some of the things I would think about and possibly discuss with your daughter in an age appropriate way.
Also, as a small adult who sometimes schools children's ponies and tries them for people sometimes, these are a few things I would be looking to buy-
-For your daughter's first pony, you need something that has been there and done it all, with a child. A younger pony that is mainly ridden by adults or older teenagers would be an absolute no-no. I would want to see the pony ridden by a child at the viewing, although obviously a lot of ponies are sold because they are outgrown.
-Get your daughter to handle the the pony during viewings and do all the things she might like to do with the pony herself- e.g. grooming, tacking up, leading etc. Pony ownership will be no fun for your daughter if the pony is not easy for her to "do" on the ground.
-Also handle the pony yourself, ideally including bringing in and turning it out yourself (at 9, especially if the riding school ponies live in large herds, it may not be safe for your daughter to do this). Make sure you are 100% confident handling the pony, as it will be you who has to step in if things are going wrong.
-Think about how the pony is kept, and the environment you will be moving to. If it is kept in a very different way (e.g. by a family with a few ponies of their own in a quiet yard) then you may face problems moving it to a different environment.
-If you think the pony is at all unsafe or too much for her to handle DO NOT let your daughter ride it at a viewing.
-Get the pony vetted!
It may take a while to find the perfect pony, and do remember a lot of the best children's ponies are a) worth a lot of money and b) are often passed on by word of mouth. Don't be tempted to overhorse her in the hope that she will improve with the pony- this is much more likely to ruin her confidence.
Get as much advice from your instructor as you can! Are they willing to accompany you to viewings, or at least look at adverts and pictures from viewings with you?
I'm not saying any of this to put you off buying a pony, as I think this sort of set up can work very well, but you really need the right pony.
Sorry for the massive essay and good luck!