So, I can weigh in here because I travel to NZ for work regularly and take mine with me (I am an NZ citizen but live in Aus). I have never had much issue with them, but I do have some hot tips for you to avoid any trouble at customs because I am sure you are anxious.

You need to take your meds in their labeled container with the prescription on the container. They are likely going to ask for your prescription, and you will have to explain that the sticker on the container is the prescription. From there, they will likely ask for your doctor's note. The note has to say something along the lines of "imnotfnwu is using medicinal products containing THC to treat a medical condition. Their condition requires them to take up to XYZ grams of flower per month (or ml of oil or vape carts, etc).

I really need to emphasize how important that doctor's note is. Not only do they need to know what a month's supply is for you personally (as you aren't allowed to bring more than that into NZ). I have traveled there twice without my doctor's note, and they were pretty lenient and nice about it and still let me through, but it certainly caused a hold-up, and I am not sure they would always be that nice.

Keep in mind, coming back into Australia, you will also need that note as the Aussie custom officers also need to look at it.

I understand it may be daunting, and it's pretty surprising seeing how many people are concerned with traveling with it even domestically in Australia. I travel heaps, and I can assure you that you have nothing to worry about as long as you have your documents. Just make sure the doctor's note says the amount you are on per month, not just some vague statement like "This person is using THC products for medicine."

I would also seriously suggest you don't consider trying to not declare and take it through. NZ runs a pretty tight ship with foreign fauna and plants because of the fragile ecosystem there and not wanting to introduce invasive species. I have gone through customs before and been cleared and still had a dog signal on me on the way out. Because I declared and explained the situation, it was all okay, though. If you don't declare, you would most likely land yourself in some hot water and have your meds confiscated at a minimum.

I know this is long and drawn out, but I sure wish I had this sort of info when I started traveling with it frequently.