This is a species of Disciseda. For some reason Disciseda sp. won’t come up on the pick list so I can’t immediately confirm this sighting.
The raggedy, non-star-like ‘skirt’ around the base of the spore sac is common fairly early but with time it weathers away. Given that I hadn’t thought of Discisedas with intact raggedy skirts when setting up puffball categories, I can see why you suggested Geastrum. My fault! I see Geastrums far, far more often than I see Discisedas and I’ve seen more old, skirt-less Discisedas than those with a skirt still present. This specimen has been photographed at a nice time while that skirt is till present and is a nice addition to Canberra Nature Map. the Atlas of Living Australia gives just 38 records for the ACT. You can see more Disciseda features at https://canberra.naturemapr.org/sightings/4208103, Disciseda australis and https://canberra.naturemapr.org/sightings/4207000. When I look closely at your photo there is a hint of the roughly reticulate pattern that I mention in my comment about the third of those Disciseda sightings. So perhaps yours is Disciseda candida – but from the photo alone I can’t guarantee it.