I've seen Janet's style of hat referred to as a "Breton", which is a broad term for a hat with a brim that rolls up. Hers is presumably wool felt with a narrow folded edge and a pleated chiffon band with an accordian bow in back.
The brim looks wider in front, and the crown acquires some dimples every time she puts her hand on her head, but I don't think the hat actually has any dimples by design - it's just a plain round dome.
The chiffon band looks pleated around the base of the crown, and then there seem to be 4 bows and two tail ends that come to a point
Look carefully in the second photo and you can also see some sort of hat pin through the chiffon band on the center front of the hat.
ETA - a hatpin is a decorative pin for holding a hat to the head, usually through the hair. A hatpin would have an entrance point (typically in back) and an exit point (typically the crown).
