Here's what it says in Therese Radic, Songs of Australian Working Life:

In his notes to *Traditional Singers and Musicians of Victoria* (Wattle Archives Series 2, Page 12) Edgar Waters says:

Tom Newbound learnt this song from Lame Jack Cousens of Springhurst a small town in northern Victoria, a few miles from Rutherglen. Cousens had travelled around farms in both northern Victoria and the Riverina with a steam threshing machine. These travelling threshing machines played an important part in the wheat harvesting, and the workers who travelled with them probably played quite an important part in spreading songs around the wheat farming districts. Jack Cousens said that he had written the words of the song himself, about a girl named Annie Waits, who lived on a farm at Moorwatha on which he had worked a threshing machine.

Gentle Annie is a parody of the song of the same name by Stephen Foster, published in 1856. Many popular songs from the American stage and concert platform were well known in Australia in the latter half of the nineteenth century, and were frequently adapted by bush song-makers to their own ends. Such songs reached Australia in a number of ways. From the time of the gold rushes of the 1850s onwards, they were often introduced to Australia by touring American entertainers belonging to black-face minstrel or variety shows, and – in the case of songs which had caught the popular taste in England – through touring English entertainers also. On the criteria commonly used for the definition of folk song in English-speaking countries, this parody of Gentle Annie is not a folk song. Leaving this question of definition aside, it exemplifies one source of tunes and texts used by bush songmakers in the latter part of the nineteenth century. Its gentle, rather playful tone casts a somewhat unexpected light on the manners of the bush workers.

NOTE: Mr Newbound pointed out that the first two lines of the second verse are a hint that the mutton had been smuggled across the border from Victoria: the songs dates from the period before the federation of the Australian colonies in 1901. The Riverina grows sheep for wool; northern Victoria also grows fat lambs for meat.

Well, there's more, but that will do for now.