Unfortunately, this island home of a number of really cool animals chose the red English (British?) lion as the symbol it wanted on the flag, along with the Union Jack seen in every other Australian state flag.
My first idea was a little lazy of me, as I thought I could get away with just putting a map on the flag, counting on the distinctive shape of the island to set it apart:
Pretend I used something other than MS Paint to create this flag, or that I used a higher resolution map to eliminate the blockiness, and this flag is only ok. The island has a distinctive shape, resembling an animal's head maybe, or an arrowhead, but even with the two northern islands, it was just kind of boring. I did some hunting through some other lesser known world flags and chose one which needed only a little color tweaking to make it Tasmania-appropriate:
This was originally the flag of Cojedes, a Venezuelan state in the north-east of that country. The changes I made were making the bottom stripe white (it had been blue) to signify how Tasmania lay just north of Antarctica, the second stripe blue (it had been black) to show that only ocean separated Tasmania from the southern ice, and I flipped the sunburst from the left of the flag to the right, which is where Tasmania lies in relation to the Australian continent. The orange and sun don't stand for anything specific, I just thought they looked good.
This may end my post on Australian flags, though if I can come up with a good idea, I'll probably do the Australian Capital Territory as well.
One last note, kudos to the interior divisions of the South American countries. The provinces of Argentina, the states of Venezuela and Brazil, by and large have really great flags. I foresee no need for a "Fix the Flags of Brazil" series of posts, because except for a few superfluous seals and coats-of-arms, they show great variety and simplicity. Bravo.