Brisbane Airport - international to domestic terminal.

You will have to collect your bags in Brisbane - the only bags that would be exempt would be for passengers in transit through to another international port (Asia, etc).

A quick search reveals this:

Catch Airtrain between the Domestic and International terminals at Brisbane Airport. It takes only 2 minutes to transfer between the terminals on one of Airtrain's frequent services. For passengers travelling on connecting Virgin Australia flights, a transfer between terminals is provided at no charge.

As codeshare partners with Virgin Australia, I expect this would also apply to Air NZ ticket-holders. I think your connection times are sufficient, even if it took an hour to disembark, clear immigration, and collect your bags.

There's a bit of a walk over to the train station and then in again when using the train for an International/domestic transfer and so it adds another 10 minutes each way for some people, especially if taking luggage.

There is also a transfer bus and that will likely leave from right outside the terminal and thus save you something of a walk, it complimentary for incoming or outgoing passengers.
http://www.bne.com.au/airport-transfer-bus

11.05 to 13.30 ought to be sufficient time for a transfer, including getting luggage and checking in.

All flights on one ticket have been well calculated. Airlines wont sell a flight if it didnt adequately cover the time between flights. After all, they arent in the business if having to put passengers on the next flight if avoidable. You should also have received instructions from Air New Zealand as to what would happen at your transfer point.

All flights on one ticket have been well calculated. Airlines wont sell a flight if it didnt adequately cover the time between flights.

Our OP could have bought the two tickets separately.

Could have. So you aren't assuming as well??

Could have. So you aren't assuming as well?? Its a fair guess given the airline and where from, its on one ticket.

I assume and infer nothing much ... if the OP needs to ask the question about the adequacy of the connection time then perhaps they were bought separately.

Nope - they were bought as one ticket. Auckland - Brisbane - Cairns. Being unfamiliar with Brisbane Airport I just wondered what the procedures were for onward travel within Australia and how long it was likely to take to go from the international to the domestic terminal.

Well, you have your answer. Yes - you will have to collect your bags, and no, it's not very far or long to the Domestic Terminal.