If you insist on putting three nuggets of information into one sentence, you need something like I was born in Hong Kong and was taken to Australia as a child, but haven't been back there since.
Thank you.
May I understand correctly?
My sentence is talking about I have never been to Australia but your sentence is talking I moved to Australia and never come back. Yes?
In that case your 'since' is misleading - I'd hesitate to say wrong, because it could be justified in a context like this:
"Ever since I was a child, although I was born in Hong Kong, I have never been to Australia."