It's a Companion kerosene heater that converts to a stove. It was purchased after WW2, some time between 1946 and 1950 probably. This matches what I was able to find on Trove. I looked for an advertisement, and failed. But I found a couple of other companies advertising similar items.
|Australian Women's Weekly, 19 August 1950, Aberdeen Pressure Stove room heater attachment.|
|Australian Women's Weekly, 8 Jul 1950, Aladdin kerosene heater cooker.|
I'll have to have a chat with my father-in-law about whether the family actually used it and, if so, where and when. And ditto for the hundreds of other items he has in his shed. He's 90 next year but it will be a struggle to get him to sit still long enough to have the chat.