You can get your little sister to allow you to do her hair by talking to her. Tell her that she looks nice in the kind of hair that she has and you would also want to have such hair then wait for her response.
I duct tapped my kids to a chair when I gave them hair cuts. Told them they'd get a surprise if they'd let me tape them to the chair. Surprise you're getting a hair cut!!! It worked quite a few times. Silly kids
Take her shopping for fancy hair bows and pretty barrettes and let her pick them out. After you get home, tell her all excitedly how pretty she will look in them and ask her if you can put them in her hair. Good luck.