It's traditional for stage productions of Peter Pan to use a woman in the title role. This goes all the way back to the original British stage productions where the decision seems to have been made for largely practical reasons. At the time, English labor laws forbid child actors from working in the evening. Casting a woman allowed them to fit more shows into the day and catch the important evening theater crowd. After this it became traditional to have a woman play Peter and almost all major stage productions afterwards have done so.
Aside from tradition, casting an adult woman as Peter has some practical advantages too. A woman will tend to look more like a young boy than most adult men will. Women also tend to be smaller and lighter than men and so will be easier to move around on the flying rigs used in the show. And while there are many talented child actors, an adult actress will probably be more experienced, skilled, and mature a performer. They will also not be subjected to labor laws regarding working conditions for children.
