Dry interior, cold front, large low pressure area, unusually strong wind.
Central Australia is a very dry place and dust storms are a common occurrence. Associate Professor Michael Box from the School of Physics at the UNSW says that while dust storms originating in this region are common, it's far less common that the dust is carried 1,500 km to Sydney. But very strong westerly winds pushed dust from the Lake Eyre Basin area to the east coast.
Professor Box says Australian dust is much redder than other dust, for example from the Sahara Desert, because of its higher iron oxide content.
http://www.sbs.com.au/news/article/1097162/The-red-sky-effect-explainedSome news sources are saying it was Sydney's worst dust storm in 70 years, so it's not like it's never happened before. Climate change may cause it to happen more often.
But there is a bright side ...
When this type of dust blows over the ocean it has been attributed to helping fertilize plankton, due to the high iron oxide content. These "plankton blooms" may in turn help to absorb carbon dioxide in the atmosphere, experts say. (Same source as quote above)
Poor baby birds, blown from their nests. However, why South Korea would want to nuke Sydney remains a mystery.