I would think twice. There is some majorly nasty stuff in some hair dyes. in germany there's some lab you can have your breast milk tested, because it contains quite a few chemicals such as brominated flame retardants from your mattress etc. I would seriously cut down on your exposure to anything potentially harmful while bf... another example would be garden pesticides, shoe cleaner, hairsprays etc.
I would think twice as well but for a different reason(hormones)I had a perm when ds was about 5 months and was breastfeeding,it turned into a mass of frizz which I am convinced was due to the hormones as it had never happened before.They say don't have a perm or colour your hair in pregnancy as the hormones may have a strange effect.You don't want your hair to turn green or something!