For what it's worth I remember my mother singing this to me when I was 6 or so [about 1945]. As I recall - a 6 year old's recollection here - it came from a song she told me was "Mother was a lion tamer".

My parents liked musical type plays and had a number of the 78 rpm "Albums" which usually would have 3 to 5 records in a sort of hard covered colorfully printed exterior art. This type of presentation evolved into tje "LP" type of jacket in the vinyl era.

I swear mom would plaay the record and sing along with it but then that was 67 years ago and the ol' mental database is a bit overloaded.