The Pattern: Sweet Little Sunhat found on the blog Hyphenated and Overextended.
My recommendation--use a bigger hook, or add a couple rows if you want this to fit your newborn well. The pattern calls for an H hook. There are instructions for making it larger on the blog. The size I made said "0-3 months." It looks more like a preemie size to me, although it's possible that I crocheted tighter than the pattern's author.
The good news about this project is that my older daughter now has a fun new hat for her baby doll!