Most of these I worked the same way. I started with an adjustable ring, worked 12 dc in ring for first round, 2 dc in each stitch for Round 2, and increased in every other stitch for Round 3. Thereafter work even (36 stitches in every round) to Round 9. Rounds 10, 11, and 12 are worked even in single crochet.
The yarn used for these hats is so adorable! It is Red Heart Gumdrop in colors Cherry and Smoothie. It's a worsted weight acrylic yarn I picked up at Michael's. I used an H hook to work these hats.
If you're looking for baby hat patterns, here are a few sites I have referenced, including my own.
Crochet Cabana - see hats for babies and children.
Kelley's Yarns (Feb 23, 2008 post) pattern in two different sizes
Cats Rockin Quick Crochet Newborn Baby Beanie (and other baby hats) has measurement information which might be quite helpful.
Bev's Country Cottage also has information on measurements
There are many other wonderful sites with baby hat patterns as well. Just do a search for crochet baby hat patterns.
Happy crocheting!
Sandie