There's a 1937 recording by Jimmie Revard and His Oklahoma Playboys here:

https://www.youtube.com/watch?v=ICSV8lQanPo

MY LITTLE GIRL, I LOVE YOU
(as recorded by Curly Williams (singer), orchestra by Jimmie Revard & The Oklahoma Playboys, 1937)

My Little Girl you got sleepy,
    and you went upstairs to bed
You put your false hair up on the dresser
    and your peg leg under the bed.
You put your glass eye up on the window.
    And your swell teeth (?) on the chair
My little girl, you know I love you
    But you're scattered here and there.

[Instrumental Break]

My little girl, you know I love you,
    and I long for you each day
My little girl, I'm dreaming of you,
    though you're many miles away
There was a time, down in the wildwood,
    Where you promised you'd be true
My little girl, you know I love you,
    and I'm coming back to you.

Note: This is a parody of a song titled "My Little Girl," which was published in 1915. Words by Sam M. Lewis and Will Dillon. Music by Albert Von Tilzer.

https://levysheetmusic.mse.jhu.edu/collection/153/161

And note that the Levy Sheet Music Collection now has recordings, at least of this song.