I grew up on a cattle outfit and "Git" was a term that meant to move and do so quickly. Usually spoken by the head wrangler or my Dad. Since cows are dumber than posts, and Englishmen were the first major owners of cattle and apparently used it in reference to someone/thing less than intelligent, I would guess that is how it became a Western slang word. "Git along little doggies" was music long before any of the testimonials written here, with the notable exception of the historical analog, I'd say it is a general word with region specific meaning. Even with a Master's Degree I still use the word when telling my dog, horses, or cows to move along. What an interesting thread!!