Hi Fred
William John BARNES b 13/12/1834 Middlesex d 16/10/1841 Sydney
Thomas Alfred BARNES b 17/4/1835 Middlesex
John Frederick BARNES b 26/9/1837 Middlesex
Elizabeth Jane BARNES b 9/1/1939 England
Mary Ellen BARNES b 9/1/1839 England - twins
George Robert BARNES b 31/1/1840 Sydney

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Elizabeth might have used 'King' as a middle name but her parents were Thomas ELLEN and Mary Elizabeth KING who were my 3rd great grandparents. She was the sister of Jane Selina CAMPBELL (nee ELLEN) who arrived in Sydney on 10/5/1863 with her children. As Jane came on an Assisted Passage, she needed a sponsor. Two independent records confirm she was met on arrival in Sydney by George Barnes. My guess is that George's mother Elizabeth was the true sponsor having encouraged her younger sister to emigrate after the death of her husband in London.
Hope this helps to clear up some things.
Ian