Tracey,
Which brother was your great grandfather then? I have records of
i William Vinson Burney was christened 1 in 1786 in Antony, Cornwall, England.
ii George Burney was christened 1 in 1788 in Antony, Cornwall, England.
iv Charles Burney was christened 1 in 1792 in Antony, Cornwall, England.
v James Frederick Augustus Burney
vi John Beasley Burney was christened 1 about 1802 in Antony, Cornwall, England. He died in 1884 in Devon (So it wasn't him).
Their father, John Burney, RN, who died 1830, was also my ancestor, through through his second wife Sarah Barker, and their daughter Emily Vernon Barlow Burney.
I would be interested in hearing more of the Australian family. You can find some information on the Burneys at Richard van Schaik's site, see
http://www.fmavanschaik.nl/kwartierstaat/pafg403.htm#81045.
I think it was John Beasley Burney who ran a steamboat company on the Thames, and had a patent for the improvement of steam engines.