True dat.
It was the Australian Flying Corps (AFC), in turn succeeded by the Australian Air Corps (AAC) in 1920, then the RAAF in 1921.
I don't think there was a badge or patch or whatever for the AAC .. and my Mum never said if there was one for the AFC (because it was waaaaaay before her time). WT still doesn't have one for the WAAAF, except the standard RAAF one that is used today. (And I only have the broken-off top of the reunion spoon one of her mates sent her.)