The other possibility is Calandrinia calyptrata, though that normally is south of the Tuross River. Its petals are 2-3 mm long. The petals of Calandrinia eremaea are 3-7 mm long.
I am not an expert, but the leaves and flowers on this specimen do not look like those of the other Calandrinia eremaea specimens on your website. My research into a photo that I have that is very similar to this suggests that this might be Spergularia rubra.