I did a partial search for the lyrics. It looks as if it comes from a western: "Check your guns" (1948)
In the reviews Here "classicsoncall" says: The first couple of musical numbers in the picture were handled by Andy Parker and The Plainsmen, but the final tune was done as a 'dueling' duet between Eddie and the pretty Nancy Gates. I wasn't sure Miss Gates was paying attention because the first line of the song by Eddie was - "You're as pretty as a palomino pony." One might interpret that as saying she had a face like a horse, but she sure looked fine to me.
The 'Eddie' referred to was Eddie Dean