M.W.
I think black hair on porcelain skin can be quite pretty in a gothic way.
You've gotten lots of wonderful advice, stories, opinions, etc. I'll just add my bit
When I was 13, I was very into coloring my hair and trying to be different. It was about self-expression and just enjoying experimenting with my "identity". My mom fought me initially, including dragging me to a salon and forcing a short, short haircut on me (to get out the black and lime green!) and then proceeding to select my clothes for a few months. I was SO sad. Not angry, just sad that she didn't "get it". I wasn't acting out, I wasn't rebelling, I was simply trying to let the world know that I really do think differently of myself and I really was my "own" person.
Finally, she realized that I was a good kid who liked funky clothes and hair. She set some ground rules for me (no shaved spots/mohawks, this was the 80s after all), and let me continue my exploration. It was a phase. By the end of my freshman year, I was wearing a "normal" hairstyle and dressing more like my girlfriends who were just not "funky"
I think what's MORE IMPORTANT than her appearance is her socializing. I didn't hang around druggies, kids who had questionable home lives, delinquents, etc. I was friends with other girls who came from mostly-stable homes and were decent students. I knew my parents expectations for my BEHAVIOR when I was home and not at home. The appearance issues were just a phase that I enjoyed tremendously and remember fondly now.
For the record, in my 30s I have normal UN-dyed hair, I wear sensible yet fun clothes (anthropologie-ish styles) and I have a tiny little piercing on my nose--something my mom totally approved of when it happened ;)