Mt Cook does RNP0.3 approaches with it's averagely equipped ATR72-500's, so Virgin should be able to match that.
They'll need RNP-AR approval to do RNP0.11
As of 15NOV, Queenstown ( & Invercargill ) was designated PBN airspace requiring RNP1.0 for RNAV STAR & SID procedures. The STAR's & SID's extend beyond the 30nm transition for enroute & terminal modes.
Big delays and holding if you want to get in there IFR without PBN equipment.
S2k