Hello and welcome to Australia and the QF FT Forum.

Domestic travel throughout Australia is free of Passport control. The only time you need to show Passports is the first landing in Oz (International Immigration). You don't need any ID for subsequent domestic flights - just your PNR or FF card should work. You'll only need to show ID if an agent is struggling with finding you in "the system". No ID needed to pass through security, and the general public can also pass security as well.

Domestic SYD T3 arrivals should be quick. I'd expect to wait at the baggage carousel between 5 and 10 minutes before bags appear. Don't expect bag priority based on status or class of travel - sometime it happens, sometimes not. Therefore, it would be very rare if you are kerbside more than 30 min after the aircraft door opens.

I only know the QF lounge(s) in BNE. But I'd expect these (especially the J lounge) to be the best option in BNE. Good food, good drinks, great coffee and the usual showers etc.

If arriving or departing on QF at SYD, you should be able to use the free QF airside transfer shuttle. But being SYD based, I've never used it - others may be able to elaborate.