Does anybody know if there is a local equivalent of the .id.au domain? Are there maybe discussions / plans for something like this?

Taken directly from the link above, here is the explanation of the .id.au domain

The id.au 2LD is for individuals. The following rules are to be read in conjunction with the Eligibility and Allocation Rules for All Open 2LDs, contained in Schedule A of this document.

 

 

1. To be eligible for a domain name in the id.au 2LD, registrants must be:

    

    

   1. an Australian citizen; or
   2. an Australian resident.

    

2. Domain names in the id.au 2LD must:

    

    

   1. exactly match the registrant’s personal name; or
   2. be an acronym or abbreviation of the registrant’s personal name; or
   3. be otherwise closely and substantially connected to the registrant, because the domain name:

       

       

      1. is derived from one or more words of the registrant's personal name; or
      2. includes one or more words of the registrant's personal name; or
      3. is a personal name by which the registrant is known.

       

    

 

It does seem like a good idea to give people their personal domain instead of trying to fit into the .co.nz domain space. And yes, I am aware of the alternate domain names such as .kiwi and .me and et al.