Kate Gagnon Osborn & Courtney Kelley answered:
This pattern is for an adult lace hat using size 5 (3.75mm) needles. If you wanted to use a size 11 needle for a child's hat, I would recommend looking for a different pattern. You can check the Craftsy patterns page here: https://www.craftsy.com/knitting/shop/knitting-patterns and use the filters on the left-hand side bar to filter for childrens' hats. I hope that helps!