I wouldn’t worry. Rather, I would stand in awe of a highly creative toddler. Only 2½ years old, she is showing a great deal of imagination. She has internalized aspects of a complicated story and is acting it out in her everyday life. I think it is amazing.
Incidentally, I notice from the ads that a new “Peter Pan” is due to be released around Christmastime. If your daughter sees it, you can probably expect even more fantasy activities related to the story. It is, after all, one that has entranced children—and adults—for generations.
I sense that you are a bit embarrassed by her imaginative activities when she is out with you. You might tell her in a matter-of-fact way, before going out, to leave Peter Pan and Tinkerbell at home: “You can play with them when we get back, but it would be better not to while we’re at the store.”
Finally, keep the books and stories coming her way. Make a weekly or biweekly pilgrimage to the public library and let her choose books. Then read them to her and encourage her to comment on them.
Our parenting advice is given as suggestions only. We recommend you also consult your healthcare provider, and urge you to contact them immediately if your question is urgent or about a medical condition.