I actually think from a business perspective they have one-up on QF, in that the cost of TT is not in any way variable. They don't have to consider lounge access. For QF, the lounges are already there and it becomes a business cost pretty easily. But for VA this would be of prime concern, as they don't have their own lounges available in Sydney or Brisbane. Melbourne is arguable, but a poor experience - they only have this the terminal is co-located, and you have to stress through security before getting to the aircraft (who knows how long it will take).
HOWEVER if they are serious about retaining traffic to NZ and making it work, they have to do the following in my opinion;
a) Offer competitive fares
b) Offer competitive connections. I don't mind flying via SYD or BNE if I have to, to get to my destination in NZ - but make sure I'm not penalised heavily for doing so
c) If TT pick up the slack, then give lounge access & ability to earn points & SC on trans-Tasman travel *only*
The biggest issue now is that right now one has a choice of 5-7 daily flights MEL-AKL, for example. 3-5 of these are NZ metal. It gets worse when you look at the smaller cities. The only advantage VA have here is firm orders for 737MAX, and a significant number of 737NG which are on lease or owned. They should be easily extended at competitive rates, if required, for use by either TT or VA. But to highlight again - if they're serious about keeping their traffic, then they absolutely need to make sure they treat HVGs the same as Qantas.
Otherwise why would anyone bother flying Tiger, when they have Jetstar and a lovely lounge next door. Neither have a domestic option once you get to NZ that is particularly attractive, so they don't have to fight for that market in my opinion.