Sorry to revive such an old thread, but I wanted mention finding a version of the song that was printed in a New Orleans newspaper in 1879. There's no "Red River Valley" there (despite the Red River of the South flowing into Louisiana). Instead, the song includes an unnamed "dear little valley." Moreover, this 1879 version had been given the title of "Billy's Parting." This makes me wonder about a uniquely Canadian source for the song. https://www.newspapers.com/article/the-daily-item-red-river-valley-11251/170546720/