After more than 1100 years of captive breeding the instincts of the japanese quail are damaged. Some coturnix do occasionally successfully brood eggs. Most often they will sit them for about 12-15 days and quit. They just don't know what they are supposed to do, so don't get discouraged if she doesn't take to it right away. Sometimes they never succeed and most wont even try to brood, so consider this a project and don't let it get you down if it doesn't work for you.
To encourage her to brood make her cage look as natural as possible and give her nest building material. If she is interested she should begin to build a nest. Try to disturb her as little as possible. Basically do everything you can to make her feel like she is in the wild, and your chances are much better.