Hi Christine,
I believe it's very hard to locate shipping information for immigration to Australia at such a late time period.
I had a look for George Cox on the Brisbane Grave Search website:
http://www.brisbane.qld.gov.au/BCC:STANDARD:229592283:pc=PC_899and these were the resulting entries (name, age, year of burial, cemetery) ...
Cox Douglas George 63 years 1992 Pinnaroo
Cox George Unknown 1888 Toowong
Cox George Unknown 1880 Toowong
Cox George Unknown 1889 South Brisbane
Cox George Alfred 3 months 1927 Toowong
Cox George Bush 78 years 1942 Lutwyche
Cox George Charles 58 years 1984 Hemmant
Cox George David Unknown 1911 Toowong
Cox George Harmsworth 63 years 1941 Toowong
Cox George Herbert Unknown 1892 Toowong
Cox George Thirkle Unknown 1920 Toowong
Cox George Thomas 85 years 1981 Pinnaroo
Cox George Thomas 86 years 1949 Toowong
Cox George Thomas Unknown 1912 Toowong
Cox George W Unknown 1917 South Brisbane
Cox George W Unknown 1945 South Brisbane Cox Henry George 53 years 1944 Lutwyche
Cox Raymond George 66 years 1986 Pinnaroo
Cox Thomas George 77 years 1996 Pinnaroo
Cox Wesley George 50 years 1966 Mt Gravatt
The only one that looks possible, given the ages, is the one in bold. I would give the Society a go for further research help, if I were you.
Best of luck!
Cheers, Brisgirl