This was the most uncertain aspect for us because we had never moved any of our stuff overseas before. So, starting from scratch, we employed our trusty friend Google for a bit of help.
We really wanted to start with a rough idea of how much it was going to cost so that we could decide whether to take all our bits and pieces with us, or to take the bare minimum and just spend an afternoon at IKEA (in Sydney, Melbourne, Perth, Brisbane and Adelaide) buying all the stuff we left behind, and probably save money by doing so.
Unless you have bucket loads of cash, shipping the majority of your stuff by air isn't going to be an option. Besides, container ships don't take that long to get from New Zealand to Australia (our stuff took just over 3 weeks in the end).
With that decision made, the next thing to think about is whether you intend to pack your belongings yourself or have professional movers do it all. Note that if you intend to pack your belongings yourself, you might find it a lot harder, or impossible, to get a reasonable insurance premium for your valuable items. This was what we found at least.
To get an accurate quote to decide if it might be cost effective to pack things yourself, you need to give the moving companies a good idea of the volume and types of things you are going to be moving.
Based on the inventory below, we ended up paying NZ$1,600 (insurance was an additional $530) for our shipper to come to our home and pack everything for us, ship it to Melbourne, clear it through Australian Customs, and deliver it to our new home and unpack everything.
Here's the inventory of items we submitted to different international moving companies for a quote:
So you can see we didn't take heaps of stuff, but it still cost us a reasonable amount of money to take our belongings with us - although less than to replace it, for sure.
You'll note that we didn't take anything very big. The single biggest item was the queen mattress, as we sold our larger appliances, lounge suite etc.
If you are planning on selling your stuff too and replacing it when you get to Australia, expect to be able to replace the types of things you can get at IKEA for less than what you might have paid for them in New Zealand if a) you don't mind shopping at IKEA - it's not for everyone, and b) you didn't get a bargain on your original stuff in the first place.