I want to suggest this girl to shave her head
Do you make these suggestions often?
No, this is a very special case.
You should not feel entitled to tell someone what they should do with their hair. Doing this makes you appear arrogant and insensitive to the desires and beauty standards that other people have.
It will be funny if she does it. Why is it wrong? I don't understand.
You may find it funny, but think about how this girl would feel if you told her to shave her head. She obviously puts a lot of care and attention into her hair, and to tell her that she would be better off without it is just cruel.