Domain name masking

I have a site residing on http://www.domain.com.au and need to forward http://www.domain.co.nz to the same site with URL masking. Unfortunately I wasn’t aware that with WordPress sites, only the index page shows with the masked URL and all subsequent pages are are shown with the base URL, in this instance http://www.domain.com.au.

Does anyone have any solutions as to how I can set up http://www.domain.co.nz so that this is the URL that appears as the address for the entire site when accessed using this address? (Accessing the site from this region will eventually have geo-targetted content).

Any advice appreciated!