I'm going to be the opposing voice here. You don't say what discipline your daughter is riding; but is she's riding hunt seat, event or dressage, I would consider a decent quality used saddle. Unless the place she's taking lessons has extraordinary school horse tack, it will be really tough to progress past a certain level without her own saddle that fits *her.*. Riding schools tend to assign saddles to horses by the fit to the horse. (The schoolie wears the saddle 15 - 20 hours per week, an individual kid only sits in it an hour or two.) That can leave an odd sized kid fighting the tack trying to learn.
Talk to her instructor about his or her recommendations. (This idea may have come from the instructor.) Then consider finding a saddle that will fit one of the animals she rides well and can be made to fit the other reasonably with extra pads, etc.,
At ten, she's going to outgrow a junior saddle (15 - 15 1/2) right about the time she's ready for a horse, so at that time you can worry abut getting something that's fits both her and future horse.
The good news is a good junior saddle doesn't lose value, you will probably sell it or trade it for exactly what you have in it. The better news is that it may *really* help her riding.
Do talk to the instructor and find out if he/she supports the idea and then go from there.