This pattern is a good way to learn the basics of double knitting in the round.

Two tips:

A lot of knitters find their headband is too big when done but few find it too small. I have found that I have to go down a couple of needle sizes smaller than I normally would use when I am double knitting. (I used US size 6 on worsted weight for this and I normally use a 7 or 8 with worsted.

Many times the inside (the fabric you are purling) is much looser than the outside fabric. I have to make a conscious effort to make sure my purls are tight.

This pattern was featured in the Double Knitting Episode
on Lets Knit2gether.