According to the media coverage, "it began in 1970, and it hasn't stopped yet. South Australia has never been conspicuously lush and wet, but decline in precipitation set in around 1970, and this decline has increased in the last four decades."
Here is a map from the Australian Bureau of Meteorology showing trends (both significant and non-significant -- the Bureau unfortunately doesn't employ basic statistical rigor in its trend analyses) in annual precipitation across Australia since 1900.
As this map unequivocally shows, almost all of southern Australia has actually seen an increasing trend in annual rainfall (i.e., getting wetter, not drier) over the past 114 years. Interesting that no mention of this longer term trend was made, isn't it? Only a tiny portion of southwest Australia is undergoing any substantial decline in annual rainfall since records began in 1900. That's it.
And even since 1970, most of southwestern Australia has seen an increasing trend in total annual rainfall. Only a thin sliver of land along the western coast has been drying over this period.
Maybe it is this type of hysterical cherry-picking by the climate alarmists that explains why "Australia's prime minister thinks climate change is 'crap' and has just abolished his country's carbon-pricing system." If climate change activists refuse to report the facts clearly and completely, politicians and other policy makers should ignore them.