Thank you very much for your replies and help. I sent an email to SIA as well, jsut to confirm what the rules really are, and they wrote me this reply:
Dear Karl
Thank you for your enquiry.
Apologies for the conflicting advise, as a Gold Star Alliance member you are allowed an extra piece of max weight 32kgs(baggage handlers won't carry more). Your free baggage allowance total is therefore 3 pieces plus 7kgs for carry-on luggage.
Kindest regards
Australian Reservations
Customer Service Centre 131011
Guess I'll print this off and bring to the airport...
Karl