It was in my garden, 25 to 30mm long, and found after dark; just a standard large black cockroach. To the eye it appeared to be almost all black, but the use of the flashlight made the red colour come out.
Looking at the Internet, I would say the most similar species was "Platyzosteria sp", eg http://esperancewildlife.blogspot.com.au/2010/07/black-cockroach-platyzosteria-sp.html
I found another specimen today, body size 33mm. You can see the reddish colour in the 2nd photo. See sighting: http://canberranaturemap.org/Community/Sightings/Details/3361078