Only because it's at the south pole. If we tilted the earth a bit, it would warm up and start raining. But if we tilted the earth a bit, Australia could probably also get wetter. As far as I understand it, the dryness of Australia, the Sahara etc are caused by the particular location from the equator, where moist air is lifted and brought to the equator and dumped there as rain. So if we pushed Australia further from the equator it would get a bit damper and maybe Indonesia would dry out.
I recommend we don't adopt this program of rotating the earth. It's almost certainly worse than just inventing fission power and pumping desalinated sea water to wherever we want to de-desertify. We'd probably also be better off if we wasted quintillions of dollaeuroyuans on a program to terraform Mars that ends in complete failure and the deaths of millions of workers over a century, but that's also an outcome I recommend we avoid.
There are lots of countries closer to the equator - they are wetter.. large body masses have continental clima, which enocourages the growth of dessert, but they usually do so only when the war of forrest vs savannah is lost by the forrest. Which can cling to areas quiet defiantly, for example the last big forrests in syria, that once covered the middle east
The dryness of Australia comes from the fact that current bring cold Antarctic water up to its west coast which leads to dry winds that blow eastward, which compounds with the complete lack of any mountain ranges to serve as rain shields to leave most of the continent dry. Even the mountains in the east of the continent are barely high enough to form a rain shield, if they were even a bit smaller then the east coast would be as dry as the rest of the continent.
Moist tropical air barely reaches the very top of Australia - instead it hits places like Java, where the abundant rainfall and numerous active volcanoes provide ridiculously fertile land that currently supports 150 million people - 5x that of Australia - despite being 50 times smaller.
