When Peter is visiting Tink in her little house, when he doesn't remember he has kids, Tink is still tiny and has very short hair. Then, when she suddenly grows into a human size, her hair seems to magically grow to her ears, and is curled. I know she's a fairy, but hair doesn't grow that fast!
I agree, why shouldn't her hair grow. And contradicting what she said, she is a fairy. Fairy's are magical, she could have done that magically. Do you really think that her normal scraggly haircut would go with that silver, sparkly dress? I don't think so!