There is a sign just past the QF lounge door that shows restrooms at the end of the corridor. That didn't exist when I was here last November.
I'm currently in SIN with a 17 hour connection between JL35 last night and QF1 tonight. Had planned to go into the city, but storms this morning and the forecast for the rest of the day, plus only getting 4 hours sleep last night made me not want to go an hour from the airport.
Went to the EK lounge for lunch when it reopened for the EK BNE flight, then moved to the QF lounge shortly before the EK lounge closed between flights, then moved to the BA lounge when QF started getting busy around 5.30.
When I was in the EK lounge, I was getting wifi from the BA lounge and when I got into the BA lounge, my laptop connected to the EK wifi. I'm thinking the back of the BA lounge is attached to the EK lounge with the emergency exit at the back of BA leading into the lobby area between EK and Plaza Premium.
I think the only reasonable space near the existing QF lounge that QF could take over is the currently public seating area at the top of the escalators.