I am trying to identify the ship in this picture in order to date the photograph. The writing on the back says it is "Aquatania" (sic) but when I search for that name on the internet the Aquitania has four funnels and this one only has two.
Having a date for that picture might be helpful, but my best guess is that is a picture of the RMS Mauretania, taken in the spring of 1940 while she was in Sydney harbor (along with the 3-funnel Queen Mary) to pick up troops for deployment to the Middle East. The paint scheme is fairly distinctive, as the all-gray was a wartime paint job. During peacetime she had a black and white paint job to help her stand out, whereas you can only see one tone of color in this photo.
Here's a photo of her underway with the wartime paint job.
Here's a website that goes into a nice bit of detail about her trip to Sydney harbor along with the Queen Mary (a 3-funnel ship). Incredibly, there's even a video showing both of them during their wartime duty, some of it shot in Sydney I believe.
Another possibility is the Queen Elizabeth, which looked very much like the Mauretania on the outside, and was also used as a troopship during the war.