Celsius and Fahrenheit in the same thread, miscommunication is sure to follow.
The Japanese Wasabi plant (Eutrema japonica, formerly Wasabia japonica) in the Mustard Family (Brassicaceae) is native to mildly cool, coastal mountain streams.
The winter lows in the OP's garden are 3º C/37º F, so that is significantly higher than the temperature where Wasabi is reported to show frost damage -2º C/27º F.
However, the heat tolerance of Wasabi is limited, with reports that it will begin to suffer above which is only 25º C/77º F, so it is quite possible that Summer heat will undo wasabi in Melbourne. Climate change does not bode well for wasabi...
Still, I am glad you are giving it a try, and please let us know the results. I would be curious to hear about any success or failure.
I'm not going to vote on the poll, as I don't usually find them helpful. It's better to consider the details than go with a simple 'yes' or 'no'.