I can now say confidently that what QEII wore in Adelaide (in the photos posted by Crowne) is definitely the badge of the Order of Australia.

One of the photos Crowne posted.


A colour image of the Queen taken after she left the Cathedral on the same day -- so taken at the same time as the photo Crowne posted.


I have no idea why QEII wore the badge on this occasion. Perhaps the government of South Australia requested it. Apparently, later in the day she and the Duke attended a b-b-q in the Adelaide Hills. Somehow I doubt she wore it then.

QEII also wore the badge, but with its bow, to a reception held at the National Art Gallery of Victoria. That event was, I believe, part of the CHOGM events.