However, the poster had forgotten Wendy Hughes (left), aka Lt Cmdr Nella Daren, love interest of Captain Picard in "Lessons" (Star Trek: The Next Generation), is Australian, albeit without a strong accent. Born in Melbourne, Ms Hughes speaks (in most of her many TV, stage and movie roles Down Under, such as Lucy Sutcliffe's niece, Vanessa Harrison, on Number 96) with very cultivated English pronunciations, similar to many Aussie actresses working in Australia in the 70s. So, anyway, there's at least one Australian Starfleet officer.
Star Trek: Deep Space Nine's Liam Bilby ("Honor Among Thieves") is also played by an Australian, Nick Tate (right), previously of Space: 1999 fame - and Holiday Island infamy! Since Bilby and his family reside at the New Sydney Colony - and a bilby is an Australian marsupial - I assume his character is also supposed to be of Australian origin (despite his American accent).
Tate was also a shuttle pilot called Dirgo on TNG ("Final Mission"), but that character is an early Michael Westmore humanoid "forehead alien". Bilby in DS9, though, definitely pays homage to Nick's human Aussie roots.
These two actors are certainly not the only Aussies to have worked on Star Trek, but Dame Judith Anderson (as Vulcan High Priestess T'Lar on ST III) and ex-Neighbours' Alan Dale (as Romulan Praetor Hiren in "Nemesis") both appeared on the silver screen in pointed latex ears!