Nah that isn't how racism worked in Australia. It was much more haphazard. Therefore there is plenty of room for differences with the Americans.
This document references newspaper articles, letters etc.
The above gives good evidence that even though Australia was literally a white supremacist society at the time they treated the African American soldiers much better than what they were used to in the US, not to say they weren't racist of course because obviously they were.
This caused tensions with the Americans and contributed to famous incidents like the Battle of Brisbane.