I think with a young child, most of the stares and comments you would get would be because they thought she'd been ill (since it's such an uncommon style for a young girl to have). If it were me, my reluctance would be based on knowing I'd get sick of having to answer "No, she doesn't have cancer," every time we went out.
I don't know. It really doesn't take too long to grow out from a buzzcut to a short-but-girlish style if it's what she wants. I guess what I would do if my little girl kept asking is to cut it short, and then shorter, and then shorter still ... and if she had a little pixie and still wanted it shorter, we'd give her a buzz. Then take lots of pictures.

It's just hair. It's not the end of the world.