The dissection was for teaching anatomy to medical students and occasionally for research purposes. The Murder Act 1752 prescribed that the sentencing court could direct that the convict's corpse be dissected (or hung in chains, but that was abolished by the picturesquely-named Hanging In Chains Act 1834).

From 1832 onward, authority to hand over a corpse for dissection was extended to everyone who had lawful custody of it so long as no relative objected, which basically meant convicts who died in prison or were executed, workhouse inmates, and the poor in hospitals, unless they had relatives who cared enough to object.

That it gets mentioned in crime stories is, I suspect, purely because it's one more grisly detail of the Bad End the criminal came to.

Full text of the 1832 Act as enacted, which only the Irish legislature's website has online as far as I can tell, it seems they don't feel the need for more up-to-date legislation on the matter. This is the text that would have been in force in all British Colonies until they got sufficient constitutional independence to repeal or amend it locally.

Go through the Newgate Calendar/ AKA The Malefactor's Bloody Register, a somewhat sensationalized history of criminals and their punishments in 17th-18th c. England. There is a pretty constant theme of disrespecting the corpse of the executed criminal. For much of the period that disrespect was gibbeting: the body would be hung in chains on a gibbet outside the town walls, in theory as a warning to potential criminals ( and indeed, in one edition the frontispiece is a drawing of a mother showing the book to her small child and pointing out the window to a gibbeted corpse in the distance). It wasn't pleasant, or thought healthy, to walk by a stinking rotting corpse on your way to and from town, and by the early 19th c. gibbeting had stopped. But "anatomizing" had sometimes earlier been part of the sentence. In 1752 Parliament passed the Murder Act, which added dissection as another deterrent to murder, expressly forbidding murderers to be buried. Note the language of punishment for Thomas Wallingford in 1752:

"Thomas Wilford, you stand convicted of the horrid and unnatural crime of murdering Sarah, your wife. This Court doth adjudge that you be taken back to the place from whence you came, and there to be fed on bread and water till Wednesday next, when you are to be taken to the common place of execution, and there hanged by the neck until you are dead; after which your body is to be publicly dissected and anatomised, agreeable to an Act of Parliament in that case made and provided; and may God Almighty have mercy on your soul!"

With gibbeting over, dissection of criminals became yet more common.

With advances in medical training and surgery, after 1800 there was also a real demand for the commodity from medical colleges, anatomy professors. That demand had sometimes outstripped the supply from the prisons, which led to the advent of "Resurrection Men", who would pull corpses from recent graves, and also to "burking:" from the notorious Burke and Hare, who would simply murder someone and sell the body. In response to this in 1832 the Anatomy Act gave medical students , colleges, etc greater freedom to obtain unclaimed bodies, bodies of paupers, etc. and put an end to Resurrection Men and burking. But executed criminals were still a resource for British anatomy teachers in the 19th c., likely the same for Australia.