I don't know about op but keep in mind it's a big country. Very close in size to continental USA. With as much climate variation.

Sydney for example has a higher annual rainfall than places that Americans consider rainy (eg. Seattle). Combine that with warmer temperatures and in many parts of Australia you are fighting a potential jungle more than fighting desertification.

Canberra, the capital, on the other hand regularly gets below freezing which means less mowing required.