I assume the one-way ticket from SIN-SYD is on a separate itinerary. You would be at the mercy of the GLA check-in agents. It is certainly possible to do so - check your straight luggage through, but if you are on separate tickets, then they are under no obligation to do so.

The fact that your onwards flight is on QF (and perhaps the EK codeshare?), would probably lean me towards saying that the agents at GLA would do it for you, if you present the onward journey details there. Do be prepared for them to refuse though, as they can technically do this.

SIN is quite a painless airport to pick up bags though, so the only thing that would worry me is the loss of connection protection being on separate tickets and the extra time you would need to allow for the onward flight check-in/baggage drop.