Okay, I went and read Spiderwomanknits' comments. Yes, she means to work another section/wedge of the 12 rows that make a segment of the hat. I believe I can count 7 instead of 6 recommended for the bigger size. I made the smaller hat and only did 5 like the pattern says and it was fine.
I also notice that Spiderwoman says to be sure to knit the wraps or you will have a holey hat. This is in disagreement with the designer who specifically says on the pattern, "(Do not knit wraps). That is at the bottom of the blue box where it says "Techniques". I did not pick up the wraps and it did not make the hat holey in any way. It did however leave little bumps on the hat where the wraps were not picked up. I figured the gal had a reason to leave the wraps unknit, but maybe there isn't a real good reason for that, and that it works fine picking them up.
About the DK yarn. DK is a weight of its own, it is supposed to be mid way between regular worsted and sport weight and be able to adapt to either, hence "double knit" (two weights it can serve as). But that said, all yarns that are called worsted, rated with a #4 in the modern system found on some skeins, are not the same. I knitted this hat with a yarn rated as #4 (worsted) but it is a rather light worsted. The yarn I used is Patons Classic Wool and the skein says it works up to 20sts =4 inches. I didn't really worry much about gauge when I made the hat, I just wanted to try the pattern. I used a size US 7 needle, the one called for in the pattern as the bigger needle. I don't know what gauge I got but the hat worked for my little 4 month old grandson. It was the smaller size and should have fit 0-6 months. It may still fit my little guy, I've never actually seen him in it, and he will be 6 months on the 19th.
I wouldn't worry about gauge a whole lot. And I think any yarn that says 20 sts=4 inches will work. Some "worsted" says 16 or 17st= 4" I think. That weight would make the hat a little bigger. Perhaps with that weight you could use the smaller directions and get a hat for a little older child. Kids vary so much.