The SYD dom J lounge is easily the worst of the QF J lounges. By the time you have taken the bus there you could be in central Sydney. For breakfast, think of the worst travelodge/motel6/holiday inn breakfast and you are about there. They do have a toastie machine though.

(no evidence of this, but I doubt they will let you take the free QF bus with an intl BP - no reason that they should not, but they do love scanning BPs, and I am sure you will hit the “does not compute”, the train is I think $10 or so for a terminal transfer, and there is a public bus which is free. You could take a taxi but I doubt the driver will be impressed.

I know nothing of your preferences and circumstances, but if you have a lunch in the city, I would be focusing on that and booking a cheapest day room at 3/4 hotel. Having access to a room, gym, breakfast etc would be more valuable than wasting time going backwards and forwards between terminals and putting bags in storage etc. Which you then need to retrieve -if you are taking breakfast in the dom terminal, where will you leave your hand luggage?

KF