Visit Art Fawcett's site, he has a hat called the Jazzman which would be about the best match I know of for that hat. I am lucky enough to own one and it has the very high crown, and nice straight sides.
I'm thinking now that the picture could have been taken in 38 or 39. She looks to be anywhere from 2 to 4, most likely 2 or 3. The hat could be a number of years older than that - early to mid thirties.
Im gonna check out that site now. Thanks for the leads, guys.