Having your shareholdings registered address in Australia when you aren't actually living there possibly complicates things for you but the following is the situation as I understand it for non-residents who have registered addresses outside of Australia.
Non-residents for tax purposes who invest on the ASX and buy/sell/own shares are not required to file an Australian Tax Return as they are exempt from CGT and any dividends or distributions paid to them have the required amount of withholding tax withdrawn from them at the time of the payment unless the payments are 100% fully franked or 100% tax deferred in which case you receive the full amount whilst any interest accrued in Australian bank accounts from such payments are deducted at a rate of 10%.
Non Residents need not act on shareholdings they own other than to indicate they are to be treated as non-residents for tax purposes, something that brokers and share registries do automatically re:TFNs as soon as you change your address to indicate that you are no longer living in Australia.
As others have said please check the ATO website and consult a professional if you wish but I can tell you the above is true and correct from my own research and my own personal situation, the major difference being the fact that you haven't changed your address which may or may not be an issue and is something you should check out.
