Can you expand your search area a bit? Maybe look into a rescue or OTTB?
This transition will depend entirely on the horse itself. You can't make a horse enjoy jumping if he doesn't naturally enjoy it, and your daughter isn't going to enjoy her experience if she's training a horse who doesn't want to jump.
That said, perhaps a general trail or ranch type, or speed/barrel bred horse will have the agility to attempt this new career? You won't want a western pleasure bred horse who will naturally chose to travel low & slow, as you need impulsion. Cutter & reiners may have more impulsion, but if they have the desire to jump, will they have the height or overall look for the H/J ring? Keep in mind that many western horses are neck reined on loose reins and asked to jog/lope, so it might take some time (and frustration to horse & rider) to get them to ride on contact at a more extended gait. Good luck!