The reason NZLARPS started was to provide a pool of funds and gear for games to draw on. It has lots of other uses too, but those are still the core benefits that make people want to run NZLARPS projects. If a region doesn't have any games that require significant funds or gear, then the benefits of running as an NZLARPS project are limited.
It's more likely that what Dunedin by Night wants is players, not funds or gear. Becoming an affiliate of NZLARPS and becoming active on Diatribe will help with that, because it will make more people aware of their existence and what they offer. There is no downside, so you could suggest becoming an affiliate of NZLARPS to them.
The other way NZLARPS could be useful in Dunedin is if someone there wants to run a game that requires up-front funds and equipment, but they don't want to invest their own money in it. Starting the larp as a project of NZLARPS will enable that. That would also get a local gear pool started, which other local larps could benefit from. It might be that there are people in Dunedin who would like to do this, but haven't done it yet because they just didn't have the spare cash or the desire to invest money into a game. I guess keep your ears open and make people aware of the option. NZLARPS is a national society, it will fund anyone in NZ so long as the project is reasonably well thought out.
EDIT: or you could start running some games as projects, and see if it spreads. You're welcome to run Camelot if you think there are 20 or so players you could gather. I have rules for running it with RPS if there was a lack of foam swords (or a local disdain for foam swords). I also have instructions on how to run it. And the props are currently in Wellington, so they're half-way to you already.