For both
Virgin Australia and Air New Zealand, this will cause a few issues.
Currently, VA uses NZ for ground handling (and I wouldn't be surprised if this changes). NZ might have to change to QF for domestic Australian connections and NZ HVC's won't be happy.
Everyone over on AUSBT is suggesting the lack of VA lounges will be the biggest issue but I think the should be quite simple:
Australia
In Brisbane (already used) and Melbourne, they can use Plaza Premium Lounges.
In Sydney, I wouldn't be surprised to see the SkyTeam lounge used (again already used for some flights)
On the Gold Coast, they've got their own lounge which potentially will be a loss for NZ who might have to sign a potentially expensive contract lounge with Qantas.
New Zealand
In Auckland, they already use the Strata lounge for some flights so I don't see why this couldn't be extended to all flights.
Christchurch and Queenstown already have 3rd party lounge which they potentially could change to.
This just leaves Wellington and Dunedin as potential gaps in the VA Trans Tasman lounge network which might require either a deal with NZ especially Wellington which is a major business route and 2 flights per day.