Assuming the following caveats the answer is yes:
1. You have status that gives you one world lounge entry or are travelling business class, ie QF Gold or higher. If you are a QF Club member, no access unless you are flying QF or JQ
http://www.qantas.com/travel/airline...global/en#show
2. The Cx flight departs at a time after 3PM, the lounge opens at 1430
As you are flying J you can access any OneWorld lounge, the CX option at Singapore is average so hopefully it's a flight that departs when the QF lounge is open. Also note they don't call the flights and you will need to allow some time for the walk, as CX flights tend to depart the pier most distant from the lounge.