their home country isn't part of the commonwealth but given they serve in the UK there's one entire group/ unit which should be on this list, too: the gurkhas
further suggestions would be:William Adams (=the inspiration for James Clavell's character "John Blackthorne" in "shogun"), David Stirling, Horatio Nelson, Jan Smuts, Arthur Shepard (spelling may be incorrect) -- an Australian soldier who spent the entire war hiding in the southeast Asian jungle with chinese guerillas, continuing to fight the Japanese rather than following the order (of his british superiors) to surrender...
more recent history: Craig Harrison and the Aussie who bested his record 2 1/2 years later, Carl Bushby and Ed Stafford
they were born when the us were still a British colony, so i'm not sure if Daniel Boone and John Colter qualify for the list...
Truganini was born on Bruny Island which is nowadays part of the land Down Under so imho she should be able to qualify?!
edit: if people who were born elsewhere but became British citizens would be qualifying for this list i'd add Hiram Maxim and Gustav von Tempsky. the former one should be well known, the latter was of some importance in 19th century New Zealand and "svord" still makes a knife named after him (which "Kiwi Bushman" Josh James used in some of his tv-shows )