Checked the National Library of Australia (NLA) for immigrants, and could only find William Jnr and Alexander, shown as :
William George Robertson, b 31/8/1939, wife Helen McGlynn b 12/7/1941, child Linda Janette b 26/2/62, departed UK by Air 11/3/1964 under Assisted Passenger Migration Scheme.
Alexander John Munro Robertson b 5/3/1932, wife Marie Neale b 15/8/1934, child James Cimon (as spelt) b 22/3/1961. departed UK by air March 1963 under APMS.
These dates of birth are not as you gave , but Alex J M Robertson must be him , can you confirm these are the correct ones. And exactly where they lived , on this site Coogee and another site Bellevue Hill ? They are miles apart .Did Christina marry before coming , and exactly who did come ? Who were Willam Snr and Mary's parents names , and did they have second name. Thousands of William Robertsons in Sydney.
Can only check NSW births to 1912marriages to 1962 and deaths to 1982. Ryerson index gives death notices to 2013, all sites are free.