For a start Qantas will check you luggage though given QF->QF, even if on separate tickets. You should be able to OLCI normally.

Also good is that SIN is one of the most efficient ports in the work for that sort of stuff.

However, as indicated, you'd be SOL if your inbound was late enough.

I would not ordinarily risk a 1¼ hour connection on the same ticket, let alone separate ones - and with a companion traveller 'who is "too old"' for insurance - simple.

Have a layover; I know there's probably nothing you haven't done/seen in Singapore that you've ever wanted, but you can still get a good meal and a good rest at the very least.