October 2016 - I just returned from a terrific month long vacation in Australia. Because I would be flying weekly while there I would need to regularly replenish my supply of distilled water. So, before leaving I contacted ResMed (based in Australia) about where to find distilled water. They told me any grocery store or Woolworths would carry it.
My first stop was in Cairns, a popular tourist destination, where I would explore the Great Barrier Reef and the tropical jungle parks. I spent my first day there trying to find distilled (aka "pure") water at Coles, Woolworths and several regular and discount chemists and pharmacies. It was not carried by any of those stores, so I settled for demineralized water. The following week I flew to Uluru (Ayers Rock) in the middle of the outback. Amazingly enough the small IGA store in Yulara stocked 2L bottles of "Black & Gold Distilled Water"! My next stop in Melbourne yielded the same results as in Cairns - but I then found a tiny IGA store and once again they carried the distilled water. The same held true in Sydney, where only an IGA store carried distilled water rather than the more widely available demineralized water.
Bottom line - in Australia use your smartphone to Google the location of an IGA market where you are staying for your easiest and best chance for locating distilled water.