Why does Antarctica receive less rainfall than Australia?
Antarctica is a polar desert and most of Australia is a hot desert. The reason why Antarctica is a desert is because the polar easterlies and the karabatic winds (winds where cold air sinks to lower elevation and soon reach the shores of antarctica where it sinks to the surface of the ocean) blows winds from the south pole into the southern oceans. These winds blow most of the moist air away from Antarctica leaving Antarctica a dry and windy place. Antarctica is also too cold for water to evaporate so storm clouds do not really form and bring precipitation into the surface. Antarctica could be one of the driest places on earth. The reason why there is snow in Antarctica is because Antarctica is so cold that whenever it snows, Antarctica would preserve its snow. This can build up layers of old snow creating glaciers and ice sheets that in long periods of time sink into the shores of Antarctica where they melt and break into icebergs.
Australia lies in 30 degrees latitude (where cloudless air tends to sink) creating drier air and the trade winds blow moist air from the Pacific ocean into eastern Australia where the great dividing range creates a rainshadow effect leaving middle and western Australia dry. The Australian desert rarely but can receive precipitation by storm clouds going through the great dividing range into the Australian desert or high pressure systems can steer cyclones and storm clouds into mainly northern Australia bringing wind and rain into the desert. The Australian desert is also hot enough for water to evaporate so it's a bit more likely to form clouds than Antarctica.