I can tell you at least the name of the last Australian convict ship used to transport convicts to Australia: the Hougoumont. She was owned originally by Duncan Dunbar, was launched in 1852, and continued to transport prisoners to Western Australia until 1867/8.

On her last voyage as a convict ship, she had 280 convicts and 108 passengers. Unusually, there were 62 Fenian political prisoners, who had been a part of the Fenian Rising, and 17 of these were, counter to normal regulations, military prisoners. You can actually view the full list [here] (http://members.iinet.net.au/~perthdps/convicts/con-wa42.html) and this might give you the last conviction date amongst them.

The book I can point you to for the most information about this ship and her last voyage as a transport ship would be Fennell, Thomas McCarthy, Philip Fennell, and Marie King. 2000. Voyage of the Hougoumont and life at Fremantle: the story of an Irish rebel. [U.S.A.]: Xlibris Corp. I was handed a copy of this not too long after it came out, by a well meaning relative who didn't quite realize I wasn't in this period of history.