I'm not aware of any proxy service for .com.au eligibility.
It is interesting to ask about as I know it is on offer for many extensions including .hk and .sg. Some proxy services void your rights to ownership however. The name would be "owned / really licensed" by the proxy service so the T and C of the Proxy service provider needs to be checked carefully.
Anyone in the world can register .co.uk, .uk, .co.nz and .nz and buy sell it as they wish.