Okay so just to get this straight in my own head, do you mean processing already refined sweet light oil or being able to process sour/heavy crude into sweet light?
In "theory", any refinery that is processing sour and/or heavy oils could convert some of that output to sweet light oils but it requires some expansive and obviously expensive infrastructure.
There's a brief explanation of the processes involved on the following page: -
https://www.afpm.org/The-Refinery-Process/#process
How many refineries in Australia have these facilities? Not many but I'm not certain for sure as I only know of two that would have been operating in the 1980s-90s period (the Shell refinery at Clyde NSW and the BP refinery in Kwinana WA). It's not like we have dozens of crude refineries though and they tend to be found in/near major cities.
I don't know if you are aware of the following site but it could be useful for you (and anyone looking to see where oil facilities are)
https://www.refinerymaps.com/