Sell my car from Australia?

Hi Glenn. Short answer. You can't.

Longer answer, you could change your membership address to Alexandra and see if that works. I think Trade Me might frown at that though if you are physically not there. The alternative would be to ask Trade Me directly for advice to see if they will allow you to do it. How are you going to arrange viewings? Test Drives? Key handover? Payment? Given you are not where the item is.

If Trade Me don't allow it you might be limited to other online or offline avenues to try and sell it.