Long term rainfall trends for Australian States and Regions
The BoM www site - Australian climate variability & change - Time series graphs - 14 charts showing rainfall variability and  set a 10 year average trend for Australia, various BoM chosen regions and the States plus Northern Territory.
Before we start on rainfall charts here are the regions used by the BoM. Note Southern Australia includes SW  WA plus Tas plus the area of Southern Eastern Australia.  For a  more detailed discussion of the regions see this Climate Change site.  I note the BoM has no rain trend for the vast area termed Rangelands in central Australia.  I am working on an Alice Springs rain history from 1874 and will also look for other long term  rain data from the Rangelands.  Vast areas of  Planet Earth are greening due to increased leaf area according to this NASA map of satellite data from 1982-2015.
There can be no doubt Australia is enjoying more rain after the early 1970's. Interesting the Millenial drought does not show big.  But our parents and ancestors  had dryer times to cope with.  There is a sign of closer to normal conditions pre 1920.
Most of our charts begin in the Federation Drought which is said to have started in 1895.
In many Australian regions and States there was very poor rain from the ~1920 to the end of WWII. I wonder if this could be termed The Great Depression Drought.

Climate research refers to the 1970's Pacific climate shift see this 1992 paper by Richard Kerr which draws attention to the PDO (Pacific Decadal Oscillation).   I think it is likely that the reasons for the often seen ~1970's  changes in rain from various Australian  regions lies with  poorly understood  oceanic and circulation factors that  caused the 1970's Pacific climate shift.
Eastern Australia had a dryer climate before WWII. The early 1970's was the wettest period.  Again the sign of closer to normal conditions pre 1920.
Looks like our monsoon strengthened in the early 1970's.  (Due to CO2 of course) I wonder if we have been using this improved rain to best economic effect?  And again the sign of closer to normal conditions pre 1920.  
The climate prior to WWII was the dryest period for Southern Australia.
The Millenial drought has been the dryest period for SE Australia and the years from the end of WWII to the early 1990's have seen the best rain.
SW Australia rain shows a long term decline.
The MDB climate was dryest before WWII. 
The NSW climate was dryer before 1950.  Can I note that there was cloud seeding  carried out after WWII. 
The NT climate was dryer before the early 1970's.
Qld shows the interesting slightly wetter than normal period before the early 1920's. 
The SA climate was near normal pre-1920 and enjoyed the best rain in the 1970's. Rain seems to be on the improve in recent years.
Tas shows a change to dryer conditions from about the mid-1970's. 2016 was a wet year no doubt welcome after dams were run down following the BassLink failure.
The Vic climate has been relatively dry before 1950 and again after the mid-1990's. Who understands these decadal changes in rain?
The WA climate has got notably wetter after 1990, also with  the normal signature pre-1920.
Chart made from data at the BoM CDO  Note the low rain years pre WWI. What caused that jump in rain in 1917? We know so little.
Just as well "climate scientists" know so much!!
The WA wheat crop does not seem to have got the message that rain is in continual decline.  Yeah yeah I know technology, improved fertilizers and farmer hard work and cunning have beaten the declining rain trend. Knocked it for six.