Actually there are two passengers on the same PNR (Passenger Name Record) with the same itinerary.
I'm surprised you won't get the taxes back. The airline has collected them on your behalf. They are not entitled to keep them although they are entitled to withhold a reasonable administrative fee.
Can you tell from your ticket (e-ticket) how much the taxes are, or tell us your itinerary so we can give an informed guess. If its less than $30 then there is no point wasting your time.
If its more I would send a nice letter to the ticketing airline's refund department asking for a refund of the taxes. If they demure then I would send the exchange to your ACCC in Canberra. They will certainly help.
The ticketing carrier should be mentioned on your ticket, they are the ones that have your money.