No idea. It is not Limosella, which usually has basal leaves, and has 5 petals. It could be in the family Caryophyllaceae, but it does not look like any caryophs in Plantnet. There is no good sideways on photo of a flower, so I am not even sure whether the flowers have petals and sepals or only sepals. If you could find someone with a plant collecting permit for your area, the best thing is to bring a specimen into the botanic gardens.
Looking more closely I agree with your comments. I own this small patch of scrub so I don't think there are restrictions on collecting. I will bring some samples to the Botanic Gardens along with a couple of beautiful daisy bushes when they flower next summer.
In January 2019 I sent a sample to Dave Albrecht and this was identified as Sagina namadgi. I will post this sighting shortly. I now think that the present sighting which had been identified as Sagina apetala is also namadgi. A distinguishing feature of namadgi is a solitary flower on a single axiliary stem. That feature can be seen in the photographs for this sighting. I have also added an extra enlargement (photograph No 4) from one of my originals to more clearly show this feature. Sagina apetala by contrast has a terminal inflorescence with 3-4 pedicels. (NSW Flora Online)