If I was you I would take this to a doll expert. Some of these oil cloth dolls are valuable.
I would agree with the approximate timeline on the doll that Rauville gave. Majorettes were at their height of popularity during that time period and little girls in the 30's to early 60's aspired to be a majorette. Having women as majorettes started in the late 1890's and was one of the few "sports" that girls could get into at that time in history. Originally a position in the military bands where they would twirl guns, it transitioned to batons and then majority females - however some of the renowned baton twirlers have been men.