Rabbits were first introduced into Australia in 1788 by the First Fleet and bred for food. The story of how they became a pest is well known leading to construction of rabbit proof fences from 1893-1997.
According to a Letter to the Editor written by “Kangarooster” of 4 January 1919 in The Courier, it was common for boys to keep pet rabbits in their yards in the 1860s. 
‘Kangarooster” writes that he lived in a ‘ five-acre tea-tree paddock, having a frontage to Main Street, near the present Pineapple Hotel. Here, when a lad, he enclosed about half an acre with a close-paling fence, and within this area had between fifty and sixty rabbits, accommodated in weather-proof hutches…’
When an Act was passed by the Queensland Parliament in 1880 making it an offence to keep live rabbits, a few fathers paid the fine rather than deprive their sons of what, to them, had been a pleasurable and, in some cases, a profitable hobby.