I was thinking that you might compare the two yarns to see the differences, the yarn you have is what you should use for a hat. Knitting a baby hat won't be a long-term project and if it turns out to be too large for a newborn you can save it for later. I think going for it is a good idea. There are a lot of patterns at ravelry and other places. Whatever pattern you choose, have fun.
Cheating is an option. . . . Cheaters never win and winners never cheat, but smart knitters who want to retain an iota of sanity do, cheerfully. ~~Kory Stamper