I have never had my carry on weighed on any QF flight. Providing that your carry on is within the dimensions for QF and piece restriction I don't think you will have a problem.
http://www.qantas.com.au/travel/airlines/carry-on-baggage/global/en
In saying this a lot of the very oversized carry on I have seen on US domestic flights would probably not be allowed on QF (a sweeping generalisation but I believe an accurate one)