As you know, all children are different. If you have discussed your daughter's shyness with her pediatrician and he or she is not too concerned, then your daughter may outgrow the shyness. But to alleviate some concerns, you can also have your daughter see a counselor and she can experience "talk therapy" to help her learn how to approach others and be more assertive.
Since your daughter has many strengths, you may want her to get involved with assisting younger kids with reading, music, computers, and animal appreciation. She could be a day counselor for younger kids at a summer camp. She needs to be in a position where she can be an overt leader with her age, knowledge, and skills. She will grow through experience by making plans and giving instructions. She will have to deal with successes and failures for her to grow in assertiveness and self confidence. Once she has learned to lead and teach younger kids, she will feel more confident around her own peers. This would be a great starting place for her.
Hope this provides a little insight. Have a great day!!!