The irony of death row inmates
When the death row inmates discovered that they were going to be spared, they were astonished. Never before had such a thing been done; Britain essentially freed the entire criminal class and shipped them off to Australia. The situational irony of that decision is truly hard to fathom.
The irony of the play
The Playmaker which the title refers to is Farquhad, the writer. His play is a broadly considered criticism of Britain tyranny. There's just one problem with him putting it on—none of the Australians can read. This itself serves as a criticism against Britain. Britain is enforcing the law, but they are not ensuring that the public services are helpful enough to prevent a disenfranchised lower class. If the criminal class can't even read, then the problem is far more systemic than initially believed.
The irony of the girlfriend
Mary is the perfect object for Baker's lusty adorations. The ironic aspect of her character is that she is a petty thief, which is ironic firstly because it seems contrary to Baker's opinions about how lovable and honest she is as a person, and secondly in that Mary literally does commit petty theft in her relationship to Baker by "stealing him" from another woman. The irony is redoubled when he leaves her to go back to Europe.
The irony of Australian life
To a person who lived in Great Britain, what must Australia be like? Now we know all about the various plants and animals, but back then, those things were just being discovered. Naturally, socially, and politically, life in Australia is the opposite of what Britain is. Britain has the pretense of education, and no one in Australia can read. In Britain, a bad winter is the worse that nature can do, but in Australia, every bug, spider, or snake can kill you. It's like an underworld version of British life.
The irony of the performance
What better day to debut the play than the birthday of the British monarch? By placing the play's performance on that day, the playwright ensures the political interpretation of his play. Then, the added factor that the civilians themselves are putting on the play, not trained actors—it's another way of saying, "This play reflects public opinion." And the opinion? That Britain is not going to be in charge of Australia forever.
