Coco,
My girl just turns two this month, she hardly have any hair at 20 months. Somehow the last two months, the hair just grew so fast and now she need a hair clip.
I would suggest you not to shave your girl's head now, I think (at least for my girl) a 2 year old girl already very concious about their outlook !!!! I don't think she will be too happy if you get her head shave.