Firstly hi and sorry for digging up an old thread !
but
I think I may have found a long lost cousin to the Woy Woy flats in St Kilda and a possible explanation for its name , I found the similarities in this local building some years back and have tried to contact the SKHS a few times about it with no success , tonight I chanced upon this thread in a Google search and thought someone here might be able to help.
When I first seen the SKHS page
http://www.skhs.org.au/skhsbuildings/42.htm on the Woy Woy flats I immediately got a familiar feeling and went out and took these photos of an old block of flats on the waterfront at Umina , I'll let the pictures do the talking........
A shot of Woy Woy in St Kilda and the flats at Umina , both are located on a waterfront parade at both have pine trees planted out front

Front view - Rear view , flats are offset on block to face bay

View of tiled wall on rooftop area and original tiled entry

Umina is located on the Woy Woy peninsula , which may explain the name of the building in St Kilda if built by the same fella , the only info I have found so far is that this building has been around since the 1940's
Appreciate any comments cheers