When I was a young kid, I had a friend who sucked and chewed on her hair.
Don't ask me why, but I tried it.
My mom told me that if I didn't stop, she would cut my hair so short that I couldn't possibly get it in my mouth.
My mom didn't mess around and I knew it, so that was the end of it for me.
You can have your daughter checked out to find if there is some type of psychological reason she is doing it, but if worse comes to worse, you can always cut her hair. There are lots of darling short haircuts. If she can't get her hair in her mouth, she can't chew on it. If she begins chewing on something else, then you have a habit that you have to deal with.
Don't do the mullet thing. If she's not embarrassed by it now, someday she will NOT be thankful you chose that option. If she refuses to wear clips or keep her hair back, a nice little bob or A-line cut is a good solution.
There really are lots of cute hair cuts that are basically care-free and super easy to manage.
I, personally, think a cute haircut is in order.
Problem solved.
Best wishes.