As anticlimactic as it is, the colony would almost certainly be very quickly subsumed by British Australia, if it even managed to last long enough to get absorbed. The first British attempts to colonize Australia barely succeeded, and that was a country that possessed a significantly larger navy and population than Sweden, as well as colonies that were relatively nearby, allowing quicker resupplies and making journeys to and from the colony less risky. Maintaining such a far-off, secluded colony in a hostile environment with such a small navy would have been virtually impossible even without the intervention of other colonial powers. Sweden also didn't have a very large population base which it could use to settle Australia with, and unlike the UK, had no use for it as a penal colony.
My guess is that they would likely settle somewhere in southern or eastern Australia in a small group, encounter the aboriginal Australians, trade diseases and either abandon the colony or, if they're unlucky, get mascaraed by a more aggressive tribe. If by sheer luck they managed to cling on for a few decades, the population would almost certainly never go above a couple thousand at the most before the British seize it and add it to their possessions in Australia.
