Here's the catalog data from Indiana University Sheet Music Collections

Title: Little child
Title: Daddy dear/Little boy and the old man
Composer: Shanklin, Wayne
Lyricist: Shanklin, Wayne
Publisher: Mayfair Music Corp.
Place of publication: New York
Date of publication: 1956
Call Number: M1 .D48 Box: 102 Item: 058
Performance Medium: Piano, Voice and Chords
First Line: Daddy dear, tell me please, is the world really round? Tell me
Chorus First Line: Daddy dear, tell me please, is the world really round? Tell me
Genre: Popular song
Subject term: Children/Babies