We let one daughter get highlights at 8 because her hair was darkening and it was important to her. It wasn't really noticeable, and she apparently got it out of her system because she's never wanted to dye it again and she's an adult now. Another daughter started dying hers at 12 or 13 and has continued to get more extreme with the colors and styles (think Cindi Lauper's 80's). It fits her personality and style, and I would hate to see her change.
Our theory in child raising was pick your fights carefully. I didn't see "style" - at any age - worth fighting about. It must have worked, all our kids have turned out well behaved, respectful, no serious problems at all.
I wouldn't get caught up over the hair dying.