In Australian English, the noun bandicoot, which designates an insectivorous marsupial native to Australia, has been used in numerous similes denoting deprivation or desolation, such as like a bandicoot on a burnt ridge.
—Cf. also the Australian-English phrase boudoir bandicoot, which designates a promiscuous male.

One of the similes using the noun bandicoot occurred, for example, in Murphy’s Man: Or Between Two Loves, by ‘Corinda’, written for the Clarence & Richmond Examiner (Grafton, New South Wales, Australia), and published in that newspaper on Saturday 23^rd July 1892:

“Where is he—confound him,” said Mr. Marston. “He has never seen Mary since the day of his arrival. He has been mooching around the station every day for a fortnight, like a lost bandicoot looking for a hollow log. Why does he not go over and ask the girl, and get done with it?”

Another simile occurred in Notes on News, published in The Macleay Argus (Kempsey, New South Wales, Australia) of Wednesday 19^th June 1895:

Parkes ¹ and Dibbs ², rumor sayeth, are again “neighbors who never speak.” Anyway, Sir Henry rambles about the floor of the Assembly like a forlorn bandicoot, grim and taciturn. He took no part in last week’s debate on the new Tariff.

¹ Henry Parkes (1815-1896) was a prominent political figure in Australia during the second half of the 19^th century; he served five terms as Premier of New South Wales between 1872 and 1891.
² George Dibbs (1834-1904) was an Australian politician who was Premier of New South Wales on three occasions between 1885 and 1894.

The simile like a bandicoot on a burnt ridge occurred, for example, in The Drover’s Wife, by the Australian author Barbara Jefferis (1917-2004)—as published in The Bulletin (Sydney, New South Wales, Australia) of 23^rd–30^th December 1980:

We had a shack out of Nyngan—my mother, my two brothers, my sister Bessie and me. Ma was a hard-handed woman. I never saw her after I cleared out with the dentist but sometimes still I dream I run into her. I’m glad to wake up.
The boys cleared out together as soon as the first was old enough. We never did hear what became of them. We had a few acres and three cows and some pigs and fowls. We made do. It wasn’t much of a life. Ma took up with a shearer when I was 14 and she cleared out for six months. It was better there without her than with her. Then they both came back and the next thing was Bessie ran off with a Bananalander. I’d like to see old Bess again; I really would, but she was never much for writing letters so there wasn’t anything I could do, not knowing where she was. She’s 49 now if she’s alive.
That left me stuck there two years with them, like a bandicoot on a burnt ridge. I gave as good as I got but I took the first chance that offered to get out of it.

The earliest occurrences of the simile like a bandicoot on a burnt ridge that I have found are as follows, in chronological order:

1-: From the following advertisement, published in The Daily Telegraph (Sydney, New South Wales, Australia) of Saturday 23^rd June 1894:

“CHARLIE, MY BOY!
Glad to see you! Well, you are looking grand! Why, wherever did you get your fat from and your color! You cheeky young beggar! Why, the girls will all be wanting to get at the roses on your cheeks! The last time I saw you you looked like a bandicoot on a burnt ridge, and now you’re as plump as a young rabbit in fresh grass. What have you been doing, my boy?”
“Oh, mother has been making me eat Arnott’s Milk Arrowroot Biscuits every day, and they have made me as strong as a house!”
These biscuits make children healthy.—Adv.

2-: From an article on Australian slang, published in The Bulletin (Sydney, New South Wales, Australia) of Saturday 17^th December 1898:

Familiar similes are as yet unnoticed. “As mean as Hungry Tyson” ³ (used by people who know nothing of Tyson). “Like a bandicoot on a burnt ridge” was, I think, applied by Parkes to a lonely and forlorn opponent. “Like a possum up a gum tree” is not bad to express quickness or cleverness in doing anything.

³ James Tyson (1819-1898) was an Australian pastoralist, regarded as Australia’s first self-made millionaire.

3-: From Joe Wilson’s Courtship, published in Joe Wilson and His Mates (Edinburgh: William Blackwood and Sons, 1901), by the Australian author Henry Lawson (1867-1922):

I mooched round all the evening like an orphan bandicoot on a burnt ridge, and then I went up to the pub and filled myself with beer, and damned the world, and came home and went to bed.

4-: From On Tented Field. The Military Camp, published in The Gundagai Independent, and Pastoral, Agricultural, and Mining Advocate (Gundagai, New South Wales, Australia) of Wednesday 3^rd October 1906:

The most laughable item on the programme was the “blanketing” of a person who wanted to know what “blanketing” was like. He soon found out. The modus operandi is this: Six or eight of the soldiers secure a blanket, and each taking hold of a part, the victim is pitched into it. The blanket is then lifted and pulled taut, and the man inside is, in consequence, shot into the air; when he falls into the blanket again the same business is gone through by the men holding it, and up he goes again. In his flight through space the victim at times assumes very funny attitudes. Jack Ah Gee, a well-known local vegetable vendor, was blanketed on Thursday. Jack was hauled into the blanket when he was looking the wrong way—for himself. ‘You killee me!’ ‘You killee me!’ were exclamations which could be heard as Gee was careering through space. His pig-tail came off, and he looked like a sick bandicoot on a burnt ridge. When Gee got out of the blanket he snavelled his pig-tail and basket and ran for dear life towards Gundagai.

5-: From one of the unconnected paragraphs making up the column Small Shot, published in The Australian Star (Sydney, New South Wales, Australia) of Friday 7^th June 1907:

Thus Premier Carruthers ⁴:—
We have to face the position that all the other States seem to be satisfied to let the Federal capital remain in Melbourne, because they imagine that it is cheaper to be there, and that they get better returns.
Then, New South Wales is playing a lone hand in this connection—remote, unfriended, and melancholy, like a bandicoot on a burnt ridge!

⁴ Joseph Carruthers (1857-1932) was an Australian politician who served as Premier of New South Wales from 1904 to 1907.