The Brisbane Airport map for the international terminal indicates that all gates are connected on the air-side and that the only way you would need to exit and pass through security would be if you enter Australia via border security.

In addition the airport information has this to say on transferring between flights:

Where do I go if I am in international transit?

Transiting between international flights in Brisbane is simple - you won't even need to leave the International Terminal. The process for connecting with your flight will depend on the airline or airlines you are travelling with, so check with your airline or travel agent regarding any visa requirements and to understand if you need to check in for your next flight.

Do I need a transit visa?

Some passengers may be eligible to transit without a visa, if they meet all of the eligibility criteria. To find out if you are eligible to transit without a visa, visit the Department of Home Affairs website.

Passengers who do not meet the criteria, or need to collect luggage and check-in for their next international flight, will need to apply for a Transit Visa. Visit the Department of Home Affairs website to apply for a transit visa.

Passengers with onward boarding passes with the same/partner airline

If your luggage is checked through to your next international destination and your airline has issued you with your boarding pass, after exiting your aircraft, follow the ‘International Transit/Transfer Passenger' signs and make your way to the Level 3 ‘Departures Area’ to board your next flight.

Passengers travelling on a different airline, needing to check-in for their next flight

If your bags are not checked through to your next international destination, you will be required to go through Passport Control, collect your luggage and make your way to Departures on Level 4 to check-in for your next flight. Follow the signs to Passport Control and Baggage Claim.

We recommend you check with your airline or travel agent about visa requirements as every situation is different.

You should check your ticket to ensure that your flight does indeed transfer baggage through to Tokyo (i.e. single ticket; I can see flights on Jetstar from Auckland to Tokyo, so it is possible that this is the case), but if not, you will need to go through passport control and check in again at the departures check-in and pass through security again.

You should check to see that you meet the Transit Without a Visa requirements (TWOV), as Australia does require transfer visas for some nationalities.

Brisbane does have the facilities for TWOV; however if you don't meet the requirements, you can find more information about a transit visa at the Subclass 771 Transit Visa webpage.

If you do need to go through passport control at any point, then 60 min is not enough. Otherwise, assuming your flight is on time, and single ticket, 60 min is plenty.

The Brisbane Airport map for the international terminal indicates that all gates are connected on the air-side, however, under Australian law, (see point 6), all passengers must be cleared before re-embarking a plane. It seems that this is on a special international transit route within the international terminal from the level 2 arrivals, so no need to go through passport control/immigration.

In addition the airport information has this to say on transferring between flights:

Where do I go if I am in international transit?

Transiting between international flights in Brisbane is simple - you won't even need to leave the International Terminal. The process for connecting with your flight will depend on the airline or airlines you are travelling with, so check with your airline or travel agent regarding any visa requirements and to understand if you need to check in for your next flight.

Do I need a transit visa?

Some passengers may be eligible to transit without a visa, if they meet all of the eligibility criteria. To find out if you are eligible to transit without a visa, visit the Department of Home Affairs website.

Passengers who do not meet the criteria, or need to collect luggage and check-in for their next international flight, will need to apply for a Transit Visa. Visit the Department of Home Affairs website to apply for a transit visa.

Passengers with onward boarding passes with the same/partner airline

If your luggage is checked through to your next international destination and your airline has issued you with your boarding pass, after exiting your aircraft, follow the ‘International Transit/Transfer Passenger' signs and make your way to the Level 3 ‘Departures Area’ to board your next flight.

Passengers travelling on a different airline, needing to check-in for their next flight

If your bags are not checked through to your next international destination, you will be required to go through Passport Control, collect your luggage and make your way to Departures on Level 4 to check-in for your next flight. Follow the signs to Passport Control and Baggage Claim.

We recommend you check with your airline or travel agent about visa requirements as every situation is different.

If you were to have check-in luggage, you should check your ticket to ensure that your flight does indeed transfer baggage through to Tokyo (i.e. single ticket; I can see flights on Jetstar from Auckland to Tokyo, so it is possible that this is the case), but if not, you will need to go through passport control and check in again at the departures check-in and pass through the main security again.

You should check to see that you meet the Transit Without a Visa requirements (TWOV), as Australia does require transfer visas for some nationalities.

Brisbane does have the facilities for TWOV; however if you don't meet the requirements, you can find more information about a transit visa at the Subclass 771 Transit Visa webpage.

If you do need to go through passport control at any point, then 60 min is not enough. Otherwise, assuming your flight is on time, and single ticket, 60 min should be plenty, though with the security clearing needed, it may take longer depending on the number of people also using the international transit facility.