Here's another pattern link
There are also directions at the end for making it larger.
Depending on where you niece likes to wear her ponytail, you could adapt almost any pattern. If you knit the hat in the round, knit flat for the length of the opening and then rejoin to continue in rounds or if you knit the hat back and forth, leave an opening in the seam.
It'd be fun to see a picture of this finished hat!