Really interesting lil things! About 1cm high, black stem and from the top appears to have four sections to which each section has the web like white mesh?. Also appeared to be living along side what appears to be little Sundews?. (I'll do a separate ID for the Sundews).
Not a fungus. This is part of a liverwort plant, probably the species Asterella drummondii. Below the cap you can probably make out a couple of blackish balls behind those white ribbons. Those balls are spore capsules. The whole stalk & cap structure arises from the vegetative part of the plant, a narrow, strap-like growth. Here are links to a few Asterella photos (the first two and the fourth show the strap-like growth, with no spore-capsules, and in the third you see a colony with numerous capsule-bearing structures): https://www.anbg.gov.au/bryophyte/photos-captions/asterella-drummondii-6.html https://www.anbg.gov.au/bryophyte/photos-captions/asterella-drummondii-7.html https://www.anbg.gov.au/bryophyte/photos-captions/asterella-drummondii-9.html https://www.anbg.gov.au/bryophyte/photos-captions/asterella-drummondii-RWP-6426.html