The RY sent a contingent to Oz in 2004 for Reserve Forces Day. There were parades in Sydney and Canberra from memory. They got f*cked around a little by the organisers of the event who are civvies and not directly associated with the Australian Army (called the RFD Association).
In Sydney, definitely hop on a ferry to Manly which is on the northern side of the Harbour. Also do the Bridgeclimb. Coogee and Bondi Beaches to the southeast are a favourite for all Poms so definitely get out there too. You will be hard pressed to find Pint glasses in Oz though. Most lagers are served in half pint glasses called 'Schooners'. A good choice is 'Tooheys New' which are New Southwelshmen's favourite drink.
In Canberra, if you are going there, definitely make time to see the Australian War Memorial. It is one of the best war museums in the world and has the largest collection of VCs anywhere.
Also, you should try and visit an Australian TA unit of the same Corps if on their Drill Night (usually a Tuesday night) you get the chance.