The small but colourful label on this perfume gives no information except R.T.Sydney written beneath an image of a large building behind which the sun is rising. As this company was based in Wilson Street, Newtown, a suburb of Sydney then perhaps that what it means but the letters R T have no meaning as yet.
In 1927 when on an official visit to Australia, the Duke and Duchess of Kent (Later King George VI and Queen Elizabeth) visited the Sydney Royal Easter Show where they accepted a gift of a crystal decanter of Goodwill Cologne from the Mayor of Sydney. The acceptance of this gift was used to promote the cologne, using the theory that if it's good enough for a royal Duchess then it's good enough for me.
Goodwill Cologne was advertised for sale in the immediate post war years but by the 1950s it seems to have been discontinued.