Every pony or horse is differently shaped, so even if they're the same height they will more than likely take a differently shaped or sized saddle. It could be because they've a high withers, are quite round (without being heavy/fat), have a roched back, etc., etc., etc.
The best thing to do would be to take a look at what a saddler would recommend (even take a look online, but obviously don't rely on it as it's hard to know who's writing it or how reliable/accurate it is. But it can give an insight into what's out there and what issues you may face.
And do not buy a saddle online. As with any saddle for any horse, you'll always need to try it on and fit it before buying it. And you'll also be able to check it for any wear and damage, such as a broken tree.
As someone who grew up living in the saddle on a shetland pony in my childhood, I can confirm that they do exist. However, it will take time to find one that suits both child and, more importantly, the pony. I think I was riding in essentially a pad saddle for a year before I got a 'proper' saddle, which I was then able to take on to my next pony. But it was quite an old saddle as I think it literally fell apart (well, not quite, but it started to become unsafe so had to be replaced) from all the use it got with me!