I believe that your Charles was the son of a Charles who was the second youngest child of Alexander McKenzie Jnr (Mackenzie) and his second wife Elizabeth Hanks - born in Bulli in 8.10.1861.
Alexander and first wife Ann McLean came to Australia with their eldest 4 children as bounty emigrants on the William Nicol in 1837 - they had 8 children in all - the last 4 being born around Fairy Meadow-Bulli in the Illawarra.
After Ann died, Alexander remarried to Elizabeth Hanks and they had 9 children - 8 were born in Fairy Meadow-Bulli in the Illawarra.
I am descended from Mary Ann, the 5th child of Alexander and his 1st wife.
Alexander and Elizabeth's youngest child Christina was born in Taralga, where the family lived for a while after leaving the Illawarra and before they settled in Canowindra-Cowra