There's also lots of us with offline resources for NSW.
Woolloomooloo is an inner suburb of Sydney, just to the east of the main CBD district. It is possible that there were events there that were regularly registered at Paddington, Darlinghurst, Waverley, Woollahra, as well as Sydney.
Registering BDM events in the 1920s, 1930s and later until the computer age, was dependent on which was the most convenient office of the NSW BDM for the person reporting a birth, death or marriage event. So, on the NSW BDM online indexes you can often find a heading "district" and then the name of the suburb/town where the deputy registrar's office received the information. NSW BDM districts quite often covered more than just the offical suburb's geographical boundaries and so NSW BDM districts are not the same as say NSW local government boundaries. NSW BDM districts are not usually the most significant piece of info gleaned from their documents.
So, basically it was not necessary to report to the nearest office in the pre computer era.
While there are no census records for you to search, there are other official records that are used regularly and are well recognised as being reliable indicators. Some electoral rolls are online via commercial websites, but there's also plenty more records (including ERs) that are searchable.
The NSW State Records Office has online indexes that cover many family history resources .... Probate Packets often include bdm certificates. Probate Packets are Deceased Estate Files that have been dealt with in the highest court of NSW (NSW Supreme Court) in the years when there were government taxes applicable to be assessed on the death of a person ..... "Death Duties"
NSW BDM certificates (or the cheaper official transcriptions) are usually very detailed, and include the information provided as to parents names, former names, nee names, ages, places of birth, length of time in Australia, details about the deceased's marriages (and naming spouse/s, children)
Here's a very good thread to have a read through, and please know that there's lots of us ready to help you find your elusive ancestors...... (Needles in haystacks seem to be a speciality on the Aussie board)
http://www.rootschat.com/forum/index.php/topic,368728.0.htmlCheers, JM