My 10 year old daughter has had a spider naevus on the end of her nose since she was 1. She is really self conscious of it too so we spoke to our GP who advised us that it can be removed on the NHS once they are over 10, but only if it is really creating an issue.
Well, when she turned 10 I asked her if she wanted to get it removed and she changed her mind. She still hates it but I think the fear of removal out weighs it.
Why don't you speak to her GP and see what they say. Because of their age having it removed in a salon is a no-no, it has to be dealt with medically.