J.,
I was diagnosed with scoliosis right around age 10 - which was 16 years ago, so it's entirely possible that things may be done a little differently now - but here's my experience. I don't remember the exact measurement of my curve, but it was higher than your daughter's but lower than 50. I had to wear a hard plastic back brace that went under my clothes (I wore a thin undershirt underneath it to prevent chafing) 24/7 for 2 years (with an hour break every day), then they gradually reduced the amount of time in the brace. I don't remember the exact schedule, but maybe it was 20 hours a day, down to 16 hours (so I didn't have to wear it to school), down to 12, and so on until I was only wearing it at night. I don't remember exactly when I was out of it completely, but I started my periods at age 12 and I know I wasn't still wearing it when I was 16.
The thing to keep in mind is that the brace will not cure scoliosis, and it will not greatly reduce her curve, it will simply help prevent it from getting worse, which would happen as she grows if she did not have a brace. A severe curve would not only give her a different physical appearance from her peers, but I believe it could lead to health problems as well.
So, as difficult as it is for children to have something "different" about them, it is for her best in the long run to get the brace. It will probably be an emotional challenge for her, as she has to adapt to this new feeling, telling her friends, etc. It shouldn't limit her physical activity very much, she'll definitely be able to walk normally, and like I said before it's worn under her clothes so it's not real noticeable. However, if I slouched a little, the top of the brace in the back would poke out under my clothes and people could definitely see that something was odd.
Here's one thing you can do to help the adjustment process go smoothly: the brace is not very thick, but it probably will require some new clothes in a slightly bigger size to fit properly, so let her have fun picking out some new clothes (but take the brace along, don't guess at sizes). It may not bother her much in the beginning - when I got mine, I was in 5th grade and it was a novelty that I told my classmates about at Show & Tell. But things changed when I got to middle school, I was tired of wearing the brace and kids started to pick on me.
I hope this helps! Let me know if you have more questions, I would be happy to help. :)