She sounds wonderful. Why should she have friends? Not everyone needs friends. Some of the most amazing people are loners and they are happy.
The stuttering I would be more concerned about. It sounds to me like her self-esteem suffers (and that's why she stutters) because she may sense that you are worried and not happy with her. Let go of your worries and just enjoy they way she is. I think this will help her the most. The book, Raising Our Children, Raising Ourselves will help you too. The author also gives counseling by phone internationally and has advice columns in UK magazine The Mother. I also saw an article of hers in Life Learning magazine form Canada, about labels (asperger, adhd ect) and she is a great guide on realizing nothing is wrong and just learn who your child is.