First of all, I live in Colorado and tried to find a sun hat for my daughter this week.  All the stores have already discounted their hats and bringing out winter stuff (and it's August).  So I hopped on Amazon and found this hat.  It is super cute w/ the eyelets, white which matches everything, and fits my 16 week old daughters head perfectly.  Many are too big.  I might cut the strings off...not sure if they will help hold it on or become a hazard.  Anyways, it has a huge brim to shade her face.  Couldn't be happier. Will definately be buying more in the future as my little girl grows!
Here is the sizing chart to help w/ ordering found on the manufacture's website.
0-6 mos
 10-15 lbs
 14"-17"
 Small

6-12 mos
 15-20 lbs
 17"-18.5"
 Medium

12-18 mos
 20-25 lbs
 18".5-20"
 Large

18-24 mos
 25-30 lbs
 18".5-20"
 Large

2 years
 30-35 lbs
 20"-22"
 X-Large

3 years-up
 35 lbs and up
 21"-22.5"
 XX-Large