At last there is some definitive information about the new .nz domain names due for release soon. If you are unsure what these are, see our article at http://www.netaction.co.nz/new-nz-domain-name-extensions-tlds/
Essentially, you can register your interest in obtaining the .nz version of your current domain name between 30 Sept 2014 and 30 March 2015.
If no-one else is using a version of your domain (like .net.nz) you should get automatic PRR (Preferential Registration or Reservation) status for the name and have no problem.
If someone else is also using a version of your name and also registers their interest, you will be in conflict and will need to make a case for an arbritrator to decide who gets the name. That may be based on whether it is actively being used, length of time since registration, trademark or branding issues etc. It may be that no-one is allowed it.
You can go online and find out the status of your domain name at http://www.anyname.co.nz. This will also show you who you are in conflict with if that is the case.
Rather than us regurgitate everything about this, there is comprehensive (and fairly easy to read) information about the whole process on the http://www.anyname.co.nz site, including the important dates, conflict issues and resolution, and FAQs.
We suggest that you should consider reserving your .nz domain as it protects it from being registered by others. But in most cases, still keep using your existing domain as your main one for your website as this is what it will be indexed as with Google and elsewhere on the net.
Please contact us it you need more information or help with this.