I don't mean chartering my own flight, but like someone else mentioned that socialflights does in the US, I was wondering if something similar existed for trans-Tasman flights.
I have yet to see anything similar to Social Flights in this part of the world, and even Social Flights appears to have closed down so I'm not sure how viable a business model it would be.
The only thing close that I've seen in Australia is EmptyJets - a site where charter aircraft operators can list flights that would otherwise be flown empty (eg: the return leg of a one way charter). Users of the site can choose to buy a seat or the entire aircraft at a substantially reduced cost.
I have seen some of the costs involved in chartering an aircraft to fly trans-Tasman, and unless you require the flexibility of a charter then it's likely to be more cost effective to book on a commercial flight - there's plenty of them (eg: up to 15 flights a day between Sydney and Auckland).