Richard, The Buckjumper is in Ron Edwards, Great Australian Folk Songs. Edwards writes,

The Buckjumper is an unpublished song from the collection of English folklorist A. L. Lloyd. He sent this to me in 1972, and I gather that he collected it when he was in Australia in the late 1920s. Oddly enough I have on tape an account of an almost identical incident recounted to me by an ex-horsebreaker.
It goes to the tune "Villikins and his Dinah."

Richard's lyrics are almost identical to the lyrics in Edwards. The only significant differences are

2nd stanza, 1st line, Edwards has: Three days she was handled, then I saddled and rode her.

4th stanza, 5th line, Edwards has: She minced up to me

"arse-about" is correct

Promised Land is capitalized in Edwards; I wonder whether that was the name of some well-known racehorse.