From one of the rental companies:
The car hire service facility is located just metres away from the
main terminal entrance of Noumea la tontouta intairport.
With Google Maps, you can see there are only a couple of car park areas at the airport, and both are within 500m of anywhere at the airport.
So the answer, I believe, would be "a short walk at ...
There appear to be at least four ways to get from La Tontouta to Noumea:
Public shuttles (navette collective), meets all flights, no reservations required but apparently make many stops to let off passengers, pricing from XPF 2500 per head (Allo Transports, Navette les Mouettes)
Private shuttles (navettes), around XPF 3000/head, from various operators; the ...
According to the Qantas website, there is one and you should have access to it -
Departure hall Level 2 - (Lift is located between the duty free collect and the bar).
2 hours before departure
Aircalin - Salon Hibiscus Lounge*
Lounge Access and Eligibility
Next onward ...