Does anyone know the Australian equivalent of 'oxyclean', please.

I think it would be Nappy San. I use the one in the bright pink plastic container. I have both the liquid and the powder but find the liquid doesn't seem to do anything wouldn't buy it again but the powder is good. It gets everything out of clothes without doing any harm.
I have even had old fabric with the yellow fold mark and soaked it overnight then washed it and it was gone.

If we're talking washing additives, I think we have something of a similar name at all supermarkets which comes in a tub like Nappywash used to be in. Supermarket chains usually have their own generic brand as well. In the Coles catalogue, Vanish NapiSan claims to use 'Oxi action'

Chemically it has some of the same ingredients as dry cleaning solvents I believe.