Perhaps there are native scats, since your photos remind me very strongly of this dung-loving species: https://canberra.naturemapr.org/species/11077. The mushroom on the shows the brown, ring-like remnant of a partial veil that initially covered the gills before the cap had expanded. On the basis of the size, colour and veil remnant I'll call it that species, while bearing in mind the ID is very highly plausible, rather than 100% guaranteed.