Hi there, and welcome to AFF!
You are correct that Premium Economy (PE) is available on QF51 BNE-SIN, as this is being operated by a Boeing 747 on the date you provided. PE is also available on QF9 SIN-LHR, operated by an Airbus A380.
As to your flight home, I'm assuming that you're departing London on QF10 (Airbus A380) at 9:30pm (29/11), arriving into Singapore at 6:25pm (30/11). This flight does have PE seating.
From Singapore to Brisbane, QF52 is the only direct flight on that date, but it is being operated by an Airbus A330-300 (333), which only has Business and Economy seating (no First or PE). Your only option for PE from Singapore on that date is to fly on QF6 to Sydney, clear Customs/Immigration there, and then change to a domestic flight - either QF508, QF510 or QF512 to Brisbane (though these will again have only Business and Economy - but it's a much shorter flight)! Personally, if you were to choose this option, I would suggest either QF510 or QF512 (QF508 is being operated by an older 767, which has only one TV projection at the front of the cabin, whereas both QF510 and QF512 are scheduled to be operated by newer Boeing 737-800WL aircraft - much nicer, and you won't feel as rushed on the ground in Sydney)... having said that, if you book both the Singapore-Sydney and Sydney-Brisbane flights on the one itinerary, Qantas should be happy to move you to a later flight should you miss the one you've selected.
I also checked Hong Kong for you, but it's also being operated by a 333, so no PE into Brisbane. Unfortunately, the two decent exit row seats on QF52 have already been nabbed, so there's no compromise to be had there either!
As an example, choosing QF6/QF510 would mean you'd arrive into Brisbane at 9:05am (instead of 7:10am in the case of the direct flight), so if this minor difference doesn't bother you or your employer, then go for it! Generally, if it's booked correctly, transiting through Sydney shouldn't overly affect the cost of your ticket (but remember to keep it on one itinerary to protect from misconnecting)!
Furthermore, with Gold status, you may be able to pre-select emergency exit seating in rows 13 & 14 on QF510 or QF512 (for the extra legroom), as all of these seats are currently showing as unclaimed on both flights.
Hopefully I've been helpful - if you have any other questions or would like me to help you find PE availability on other routes and dates, I'm happy to do so