More commonly “happy hunting ground(s)”, which does get a mention in the OED (s.v. hunting-ground), and in Wikipedia, but there’s no clear indication of an Indian language source. First citation is from Cooper’s Last of the Mohicans.
See this Straight Dope Staff Report for a more extensive, but still inconclusive, discussion.
The Wikipedia article begins with the claim “The happy hunting ground was the name given to the concept of the afterlife by several of the great plains Native American tribes, such as the Iroquois, Cherokee, Algonquian and Sioux,” but no citations are given in support of this assertion.