The Loafer's Glory programs are available for listening and download here. Andy's Gone With Cattle starts in at about 30:30, and you can skip directly to it. I'm sure that's not Priscilla Herdman, it doesn't sound at all like she does on Water Lily or any other album. It's the same tune Herdman uses. Phillips attributes the tune to Slim Dusty, but I think he was mistaken. Bob Bolton, upthread, and Chris Kempster, in The Songs of Henry Lawson, both write that the tune is trad, collected by John Manifold.