True, with the exception of Tasmania and southern Victoria which feels like it has been cooling for the last 18 months, we have had few days above 30°C down here & usually the grass is scorched this time of year, but it is still green 
It may be cooling for the last few months, but no one knows when the next major drought is about to come. Australia has suffered numerous droughts during the past two decades, and I suspect that the main reason for that is climate change.
High temperature means a higher saturation point for water vapour. So more amount of water vapour will be held in the atmosphere. But eventually, this water vapour will be converted into rain or snow. But the problem is that rain occurs only where a stream of water vapor meets with cold air. Such regions exist mostly along the tropical forests. So for the other areas, there will not be any noticeable change in the rainfall.