From an online dictionary:

In Western Words Ramon F. Adams gives one possible etymology for dogie, whose origin is unknown. During the 1880s, when a series of harsh winters left large numbers of orphaned calves, the little calves, weaned too early, were unable to digest coarse range grass, and their swollen bellies "very much resembled a batch of sourdough carried in a sack." Such a calf was referred to as dough-guts. The term, altered to dogie according to Adams, "has been used ever since throughout cattleland to refer to a pot-gutted orphan calf." Another possibility is that dogie is an alteration of Spanish dogal, "lariat."