Where were we? Ah, yes ... hedonism and hubris. The urban myth goes that Sydney oozes H & H whereas Melbourne is content with elegance and culture. Meh ...
I think I have sorted out what that cute little building is. There are two tidal gauges on Sydney Harbour. This is one of them. The other is on Fort Denison.
According to the Dictionary of Sydney:
The calm water and ease of launching small boats meant that the northern end of Camp Cove was used as a base by the water police after they were relocated from Garden Island in 1840. The foundations of the wharf used by the water police from 1842 now end in a tidal gauge.