Looks like QF and APAM have a specific agreement about their airport fees and charges, so its not listed on google.
So, probably QF is able to save a bit, maybe they get a discount for T1 arr and dep pax overall.
But they still have to remit the money to APAM (Aust Pacific Airport P/L).
But for T2/T3/T4, airport fees and charges account for about $28 to $30 of fares charged by the airlines to us.
No way to escape these.
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Edit:
I would fly VAd J on that day, or the lower fare and pay for lounge access, have done it before in the past, for that $399, as mentioned below.
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Cut and paste from Jpp's reply below:
What date are you looking at specifically, Thursday 20 October? When I check Virgin it's $309 for that 4:40pm flight, and business class at $399 . The $309 for economy is on the high end but far from unheard of... I can't get anything near $699 to come up.
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Also, the 5:45pm flight on Qantas is $491, certainly expensive but a lot better than the $928 one at 4pm. (If you really must go at 4pm, maybe you could at least pay $1044 for business class!).