More than happy to go with Rainer's field ID, though it is a bit unusual that there are no signs of flowers or fruit at this time of year. Worth checking in again in as the year progresses to confirm the presence of fruit or flowers. Thesium will often "disappear" over the winter months so don't panic if you can't find them in June.
Thesium is usually a more grey green than the plant in the photo. It turns yellow/golden as winter approaches. Stackhousia is more a dark green. The leaves of Thesium are 0.5-1.5mm wide. Stackhousia are 2-4mm wide. I really would expect Thesium to have fruit in the leaf axils at this time of year whereas Stackhousia have usually shed their fruit and dropped their flower spike by now. Thesium is decribed as grwoing erect but in my experience it trails along the ground and through the grass whereas Stackhousia is very erect. Whilst the habitat you described is good for Thesium (dence Themeda) it is generally in wetter areas patches or sites with higher rainfall. My guess would be that this is Stackhousia.
The greenish yellow narrowly linear leaves, lack of spent terminal inflorescences and sprawling habit are all good for Thesium. Lack of flowers or fruit may just reflect the previous dry conditions that meant that flowers didn’t appear this year. None of the stems we observed had any signs of lack of previous flowering in the form of the terminal inflorescence.
In contrast, there was a Stackhousia nearby, with a spent inflorescence. Locally, Stackhousia monogyna has darker green, more succulent and broader leaves, and the nearby Stackhousia with its darker green fleshy leaves matched that form.
Ive now had advice from Lachlan Copeland, a NSW botanist, who has confirmed that this is indeed Stackhousia monogyna. Here’s what Lachlan said: “… this one is definitely a Stackhousia...stems and recurved leaf margins no good for Thesium.”