So why are the soils red in Australia, while the soils of many other parts of the world are black or grey?
The nature of soil depends on many factors like climate, time, composition of the rock from which the soil forms, and others.
In cool climates the rock weathering is mainly physical, while in hot climate, chemical weathering is more common. One form of chemical weathering is oxidation, and most of Australia has got a perfect dry oxidising environment. It is the oxides that make the soil (and the rock from which the soil forms) red.
Another factor is time. Large areas in the Northern Hemisphere experienced "recent" ice ages where glaciers scraped off the soils and exposed the bedrock as they moved. There, the soils are only 1-2m thick and no more than 5000 years old.
With the exception of Tasmania and parts of Victoria, Australia hasn't "recently" (geologically speaking) been affected by ice ages, and most of Australian soils are very thick and millions of years old, so the remnant iron oxides have accumulated after millions of years of weathering.
But no matter how colourful the red soils make the landscape, there is not much use of them because they are very poor in nutrients. The black soils of Northern Hemisphere are much richer in organic matter than the red soils of Australia.
NOTE: This website is written in British English, which is the English we use in Australia. You will find words like "traveller", "harbour" and "realise", and they are all correct in the language used in Australia.