Gustav III escapes his assassination in March 1792, and follows through with his sponsorship of Bolts' venture to colonize Western Australia; with the Australian colonies subsequently utilized by the Swedes in the same manner that of the British used theirs, but to a even greater extent. It had been with the Riksdag of 1786, and his subsequent passage from semi-constitutionalism to semi-absolutism, that his foreign policy had become more adventurous; in doing so, Gustav had aroused popular indignation against the mutinous aristocratic officers, resulting most infamously in the Anjala Conspiracy to declare Finland an independent state, but Gustav III ultimately quelled these rebellions and arrested the leading conspirators, with public opinion on his side. Capitalizing on the powerful anti-aristocratic passions thus aroused, Gustav summoned a Riksdag early in 1789, at which he put through an Act of Union and Security on 17 February 1789 with the backing of the three lower estates. This reinforced monarchical authority significantly, and further inflamed the nobility's hatred of the king. Most of those aristocrats who were found to be conspiring against him, and convicted of high treason, were sentenced to death; but only one or two were actually executed, with the overwhelming majority either sent to prison or deported. And in Russia and Denmark, where most of them ended up, they were far from isolated, continuing to incite regicide against him.
So, where better to send all of these rebels, dissidents, political prisoners and independence activists, instead of into the open arms of Sweden's enemies, than to his newly established colony in South-West Australia? Given that he agreed to sponsor William Bolts' proposal to colonize Australia immediately after the Riksdag of 1786, within less than a week of it, it seems fairly likely that this was the chief motive and incentive behind Gustav III's desire for an Australian colony in the first place. And remember, in the Third Coalition against Napoleon, Sweden and Portugal were Great Britain's only European Allies against Napoleon, after Russia allied with France. Considering events closer to home, Sweden's status as a critical British ally, and that the Swedish colony's in a location which the British were deeply concerned that the French would lay claim to, I'd say they'd have a more than decent chance of the British being fully supportive of the Swedes' claims to Western Australia. They'd be the ones keeping it out of the hands of the French, after all; and it'd lighten the British Royal Navy's own load. Would it be profitable as a colony, or trade post? Probably not for a while. But it'd be immensely valuable in maintaining the coherence and stability of Gustav III's revived Swedish Empire, especially in its early stages.
The British had the Irish that they wanted to send far, far away; the Swedish, at this stage, still had the Finns to fill the same role. And as such, with the Finnish nationalists all deported to Western Australia, and Swedish Australia having a Finnish majority, it's Finnish, not Swedish, which becomes the majority language in Western Australia ITTL.