It is required by Australia that its citizens travel to/from Australia on Australian passport. It is not like Canada.Al though, it is not REQUIRED by Australia (just like Canada), it's the best and easiest option. You can carry your Australian citizenship documents too, but if I were you, I'd get an Australian passport.
Have you read the OP? The OP has the citizenships of Australia and the USA. Australia requires its citizens to use Australian passport when dealing with Australian passport control, regardless of how many other citizenships they may have. The USA has exactly same rule.Your passport should be from your home country, If you have US passport that means you have the citizenship in US, So you can travel Australia with your home passport.