I spent a half hour or so, just now, trying to figure out where/when it entered common usage. So far, all I find suggests it dates back to the early 1800s, and that it is a paradise or heaven for American Indians....
Personally, I intensely dislike the phrase. Ann Rinaldi used it in at least one of her books, and I just ran across it in Lois Lenski's Indian Captive: The Story of Mary Jemison, first published in 1941. On page 59, Lenski writes:
After a time their grief subsided and they rejoiced to remember that their brother had gone to the Happy Hunting Grounds above the sky.I'll spend more time digging on that phrase... Who said it first? Was it an American Indian? What tribe? Why? Skeptic that I am, I'll bet it was a non-Native person... A writer perhaps, or maybe a hobbyist! The hobbyists were (and are) pretty prolific at coming up with "Indian lore."
Update at 8:40 PM: Amazon has a nifty option, that allows you to search the text of a book. On a hunch, I searched James Fenimore Cooper's books and found he used "Happy Hunting Ground" in Pioneers, on page 760. That book came out in 1823. (Last of the Mohicans came out in 1826.) Any librarians reading the blog? If you can find an earlier reference, that'd be terrific!