I just finished this cute little brimmed hat with strap and even found the perfect matching buttons - with a little help... Jp's my resident expert button picker:
Isn't it just the cutest? It should fit a baby up to about six months old. I've just sent off some photos to baby photographers I know in case it's something they want for their prop collection and then it's off to my Etsy shop.
The creator of the pattern has allowed makers to sell their finished hats as long as you link back to her so if you are interested in making one yourself here is the pattern link (plus you get to see it on a real baby!)