Seduarte: Your song is a different one, but certainly worthy of having at Mudcat.

The Online 78rpm Discographical Project says LITTLE CURLY HEAD IN A HIGH CHAIR was recorded by Ben Bernie & His Orchestra, on 3/28/1940, and released as a 78-rpm record, Conqueror 9461.

Another discography indicates that Gracie Fields also recorded it in 1940.

The title is usually given as LITTLE CURLY HAIR IN A HIGH CHAIR. Under that title, it was recorded by Ben Bernie (on the Vocalion label), Eddie Cantor, Jimmy Dorsey, Sammy Kaye, Johnny Messner, and Fats Waller—all around the same time in 1940. Helen O'Connell also recorded it, but I was unable to find the date.

The Red Hot Jazz Archive has the recording by Fats Waller: Click to play.

It was used in the 1940 MGM film "Forty Little Mothers," directed by Busby Berkeley, and starring Eddie Cantor. IMDb.com gives this info:

LITTLE CURLY HAIR IN A HIGH CHAIR
Music by Nat Simon
Lyrics by Charles Tobias
Sung by Eddie Cantor
Played often throughout the film
Reprised by Eddie Cantor, Judith Anderson, Rita Johnson, Nydia Westman and schoolgirls