Bobad, the only 'correction' I'd make to the lyrics you posted is that (at least in Tessie Brewer's version and in the sheet music I've seen) the first verse says "havin' you," not "lovin' you."

And, yes, the tune is derived from a much older musical piece. That it's a Hungarian Rhapsody by Lizst sounds right to me. Of course, I also have read that his Hungarian rhapsodies were themselves derived from older folk tunes.

I also get the feeling, based on how popular this song is with the centenarians, nonogenarians, and other elders I've been doing music with for a long time, that the 1950 versions were covers of an older popular hit.