My understanding is that separate PNRs make the traveller responsible. Right now I am in a similar situation with LHR-SYD return on one PNR with SYD-NAN on a separate one. My main concern was the return from NAN - SYD because of FJ performance in the past. Like you I considered flying a day early to SYD and spending an evening out on the Rocks. I found a good travel insurance policy however which covers losses experienced by an "independent traveller" in the event of a missed connection on 2 PNRs. I called the insurance broker to specify exactly what I had in mind and he assured me that the policy covers this eventuality.

The policy is with John Lewis, take a look at policies for the independent traveller.

Alternatively when you book with Qantas you are offered QBE insurance but I am not sure if this covers consequential losses arising from missed connections on separate PNRs.

If you choose to stay over in SIN then take a trip to the zoo for an evening tour, it is really interesting.