We've discussed exploring other extracurricular activities (e.g., music, tennis, or golf), but, so far, she's managed to avoid getting involved in anything that she doesn't succeed at immediately. Without any PE at school, we believe it's important to encourage participation in physical activity. What should we do?
As for wanting her to have more physical activity because of a lack of PE in school, consider doing more pleasant physical activities as a family -- bike riding, hiking, power walking, swimming, etc. Little League, or any other athletic activity, should be pursued first because your daughter shows an interest in it rather than because of the fitness benefits. We tend to stick to activities that give us pleasure. I am sure that she will find such activities if she is allowed to sample what's available.