I've done very little english riding myself, and the last time I was in an english saddle I got thrown, so it's never been my thing. She has a trainer to work with, and her quarter pony does have a pretty bouncy trot, so english will probably be better all around.
My question is, when looking for an english saddle for her, what kind has the deepest seat? I'd feel more comfortable if she were starting out in a saddle with a little bit deeper seat. Or maybe that's just me being a worry wart? I ride my green horse in a barrel saddle (I have no intention of ever doing barrels) because I feel less likely to fall out lol. So I don't want to "project" my anxieties on her if it's not a relevant concern.