If you have provided proof of course offer and fees paid, insurance in place, $15,000 NZ in your bank account for maintenance/accommodation, IELTS if required, this should be fine. It is possible that they will want more, but I can't say. If it has only been a week since it got to INZ it will probably be at least one more week, maybe 2. If it does take time, I suggest you contact VUW and explain that you are still waiting for your visa. They may be able to be slightly flexible on arrival date so long as you have kept them informed. It's much better to be there for the new student orientation but so long as you are not missing vital course delivery, it should work out.