Does the melody sound similar to the song sang here? http://blackballing-timtebow2.blogspot.com/2012/11/thanksgiving-turkey-drumstick-jack-o.html

I've found two articles which date the song to before 1935; see:
- Spokane Chronicle, June 28th, 1935, p. 4
- Brooklyn Times Union, November 17th, 1936, p. 23

Both, unfortunately, don't specify an author, with the latter even saying "Author unknown"