Acai is tropical in its requirements. In Sydney it would probably be safer to grow the closely related E. edulis, which is much more cool tolerant (should be ok in frost-free parts of Tassie). The berries have similar qualities, I believe. There is a lot of information available on the web.

The 'edulis' part refers to the palm heart btw. I had a good sized seedling with about 500mm trunk height whihc I dropped an Acacia tree onto a few years ago. The palm broke off neatly at ground level. It was dead, so not wanting to loose everything, I ripped the crownshaft apart and ate it. Very very good. I want more!

E. edulis (striped trunk centre left) growing in Auckland NZ;