X.X.
Personally, I would seek other ways to support her. Shaving my head would draw far too much attention to me and I don't think i could deal with everyone asking me what happened or why. I'd rather have the attention go to my friend and use my time/energy doing something for her that can really help. Cooking dinners, cleaning or mowing her yard, watching the kids, shopping, or just taking her to a movie to forget about like for a while are all productive alternatives. Sometimes the smallest things can mean the most.