Ask anyone who is not a resident of Australia to look at an Australian flag and say which country it belongs to, then point to a Qantas tail and ask them whose it is, chances are 1% will get the former and 99% will get the latter.
The reason the Canadian flag is so well recognised is that it is so simple and uncluttered, displaying the maple leaf as it does.
We also have a symbol that is exclusively Australian and that is the kangaroo, a simple flag with just a red roo on a contrast background would eliminate all the racial divisiveness, with nothing to remind of the colonisation by Britain, and no need to add this flag and that flag, just one that says 'Australia', no matter what tribe you are from.
Have a look at the Norfolk Island flag, just a clean green Norfolk Island Pine on a green and white three panel flag.