With the "pinked" edges and the graphics of the printed fabric, I'm thinking homemade, roughly mid-century. Say 1940-ish. Is the brown side a cat?
Well, I do know that these dolls appeared around 1900... there are various theories as to their origin/meaning. They reached kind of a hey-day in the 1040s-50s. During the mid 1900s, McCalls, Vogart, Redline and Butterick pattern companies began producing their own Topsy-Turvy Doll patterns. Vogart's pattern in the1940s was titled, "Topsy and Eva Doll--One doll with two changeabout faces." Redline's pattern in the 1940s was called Topsy and Eva. So there were lots of home-mades. They were actually still made up into the 60s. Controversial, obviously. My guess would be that yours is pattern-made, mid-century, unless somebody knows better. You might research those patterns and names... to see if you have a match, but... that would be a real challenge. EDIT We can agree on that, Abuela!!!
OOOOOOOOOOOOOOOHHHHH! That sounds like a good diagnosis! EDIT Annnnnnnnd... they're out there. Time frame probably similar.
Just as a historical note, the "Topsy and Eva" reference is to a 1927 movie, featuring the Duncan sisters, Rosetta and Vivian, based on their vaudeville act of the 1920s. With Rosetta in blackface they performed an act loosely based on the characters from "Uncle Tom's Cabin." The 1940s patterns based on the characters could probably be customized to suit the maker, and I can't tell if these were intended to be a cat, wolf, or what. One of them does have a distinct Red Riding Hood appearance, so wolf might be a good guess. See http://utc.iath.virginia.edu/onstage/duncanhp.html (from https://en.wikipedia.org/wiki/Topsy_and_Eva original copyright United Artists)
Thanks, Fakesie... I didn't know the whole story. Yeah, I think we have a custom RedRidingHood and Wolfie (What Big Ears You Have, Grandmother!).