I purchased this for a family vacation with our five month old, as we were going to a sunny tropical climate and wanted to shield her from the sun. The problem I found with this hat is that it is made of synthetic material and hence does not breathe, and the baby's head gets very sweaty and hot under it. It ended up balled up in a corner of the luggage, and I used an all-cotton sunhat I received as a gift instead, which worked much better.
It would have been nice, because the shape affords more shade than a typical baby hat, if not for the ventilation issue.
I was carrying her in a baby bjorn. Maybe the overheating from the hat would be less of an issue if the baby is sitting in a breezy spot, but that limits the hat's usability, imho.