Yes, they definitely interline (or at least they did two years ago).

In 2006, I booked two award flights BNE-SIN ( Star Alliance award in Y) and then SIN-LHR (One World award in J) with a 2 hour connection time. Singapore Airlines tagged my luggage through to LHR. All that was required at SIN was a visit to the transfer desk to pick up my onward boarding pass for the BA flight.

Singapore and BA/Qantas use different Terminals at Changi - so make sure you go to the Transfer Desk located in the same Terminal as Qantas to pick up your boarding pass.

Extremely easy and quick - still had plenty of time to spend in the Lounge.

I called Singapore Airlines before I departed to confirm this wouldn't be a problem. ( Perhaps call them also to alleviate your fears - just in case policy has changed)