Inconclusive sighting

Mostly, the fungal photos that appear on Canberra Nature Map (mushrooms, stinkhorns, polypores, etc) show the structures that produce sexual spores. Many fungi are known to produce asexual spores, via structures that are (a) of much simpler construction than those that produce the sexual spores and (b) much smaller than those that produce the sexual spores. The visible (sexual or asexual) structure is produced by an out-of-sight network of microscopically fine threads (or mycelium). A given mycelium may produce the sexual structure under certain conditions, the asexual under other conditions (or both simultaneously). Because the asexual and sexual spore-producing structures are usually quite different, you find that in the 1800s and into the 1900s, the structure that produces asexual spores would be assigned to one genus, the sexual to another. In essence, one organism was given two different species names, one based on the structure that produced the sexual spores and the other based on the structure that produced the asexual spores. The fact is that, in pre-DNA days, to prove that two structures were manifestations of the same fungus required lab work, starting with the spores of one form and showing that you could produce the other form - and a lot of names had been created before lab work revealed the relevant sexual-asexual connections. I think this photo shows an asexual form. Identification would need microscopic study of a specimen. On the habitat and based on probabilities, my initial expectation is that this belongs in the genus Chromelosporium. In that case, the sexual spores are likely to be produced in rubbery, brown to blackish brown cup-like structures of the genus Peziza, each perhaps a centimetre or more in diameter. There's an outside chance that the photo shows Ceratiomyxa fruticulosa (a myxomycete, ort slime mould, which is not a fungus despite the word 'mould').

So the only way to determine the species or genus is to DNA test them or analyze the mycelium under a microscope?

Microscopic examination of the visible white stuff (not the hidden mycelium) should get you to species. There is structure there, but it is minute and doesn't show in a photo. There are, undoubtedly, some difficult cases where microscopic study may still leave you unsure and where DNA evidence may settle the issue. In my earlier response I noted DNA as a means of trying to match an asexual state to a sexual state, without having to go through the process of growing fungi in the lab. These days, with DNA testing much quicker and cheaper, people can extract a DNA sequence and look for a match on a database of DNA sequences, in less time than it takes to grow fungi in the lab. A mycelium is fairly featureless under the microscope.

Thanks Heino excellent information re sexual and asexual fungi forms