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.