You're right!

It is an important step that Kate is willing to go to talk to the school nurse. The nurse will be able to give her advice on how to involve her parents. You should give Kate the chance to talk to her parents before you call them. If she DOESN'T talk to someone or you are worried about her safety, then you can tell her parents yourself. She may feel safer if you offer to go with her to talk to the nurse and her parents.