purchase upgrade
 

I've tried to find with the search tool but no answer.

Is it possible to purchase an upgrade (with cash) at the check-in or at the gate ?

In general, you can always pay the fare difference between what you paid and the fare for the class of service you can fly on. This needs to be done at the "ticketing" counter at the airport.

Check-in / gate agents generally don't know how (or are authorized) to do fare calculations.

It might be better if you do it at the time of booking.

It depends on your booking class. Some booking classes do not permit any paid upgrades unless the flight is overbooked.

This describes changing or upgrading a ticket. I think the OP was asking about gate/counter upgrades that some carriers offer which I don't believe OZ does.

Most US carriers offer such upgrades but the product & service is usually quite a bit poorer than the better Asian carriers. Still great to be in C/F than Y on a TPAC or TATL route.