So if you get one that hasn't been pushed to walk fast, you might be alright. If you get one where the trainers/riders have been pushing the walk (and they can have a very fast natural walk) then you might be riding the brakes so your daughter can keep up. Unless she like to trot, which I did when I was a kid.
I actually bought a Fox Trotter so I would have a horse for gaited rides, and I have a Mustang for QH rides. My Mustang would just rather not walk fast.
As far as the breed goes, I'm sure a Walker would be a blast! I've ridden one and several Fox Trotters and they are oodles of fun as well. It's like you have all these extra gears that you have to learn how to use, and it's fast and fun. I LOVE the gaited horses, it's just sometimes the gaited riders irritate me!