The index to birth registrations is available online to 1911 and offline to 1918. Any events outside these dates are not open to public access.
I don't see Thomas Henry and Mary Lavinia at the address you have given in your post.
1937 - Edward St, West Sydney
1943 - 110 Illawarra Road, Marrickville
1949 - 132 Salisbury Road, Annandale
Thomas was a baker. They were still living in Salisbury Road in 1963 and it looks like Thomas died in 1965. Mary is still on the electoral roll in 1980 so it is more than likely that she died post 1981 which is the extent of the indexes. Born in 1894, she would have still only been 86 then.