
The song was written by John Rox (1902–1957) and was wonderfully performed by 10-year old Gayla Peevey.
A local promoter in Gayla's hometown (Oklahoma City) followed up the national popularity of the song (it hit the top of the charts that December) with a campaign to present Gayla with an actual hippopotamus on Christmas.

The hippo, by the way, was a featured attraction there for nearly 50 years.
But enough trivia. Here's the original song as I first heard it in my pajamas as a two-year old kid.