Welcome to Oz when you get here.

How much choice do you have on airlines/routes/fares? As above, a lot depends on the economy tickets. The economy price can vary a lot. As can the t&c's. Any "upgrade" cost difference could be getting close to the full retail business fare. Getting the cash from the employer and doing the rest your self would be the simplest. However the AU employer, if they have a corporate travel deal, may be paying a less the public retail fare.

Guess AY mentioned as they seem to sell BNE-SIN (AY codeshare QF operated) SIN-HEL-UK.
If you want to fly direct into BNE Qatar QR is another Oneworld option. Will be other options via SYD and even MEL. BNE has less international flights than SYD MEL.
Look here (may not be up to date)-->https://en.wikipedia.org/wiki/Brisbane_Airport

I suspect upgrading 4 people on the popular Kangaroo route with any ff currency will be hard/impossible. Even those with top status on QF/BA find that hard for 1 passenger.

Edit
For a random June 2022 date LHR-BNE from google flights:- business- premium economy - economy. Possible to show more flights.
A UK origin other than LHR will show different options.
Some people, who have company paid flights, will work the system to show what want (prices, route, etc)