We moved when our children were 18 months & 3 - was a great time to move as the boys were very easy to settle into a new area and lifestyle.
Advantages - I already had a permanent job with good salary; we moved to a great area (not Wellington or Auckland!), weather (maybe not this year but in general), fresh seasonal fruit and veg, excellent health and education, biking / tramping / kayaking, commute went from 3h to 8mins by bike so I see a lot more of my family than when I was working, we can afford to live on my part time salary so I get more time with the boys and DH can be a sahp.
Disadvantages: it’s a very very long way away from anywhere else and the distance is very real when someone in the UK is ill or as parents age. You need a decent job, house prices are rising especially in the cities, there is more and more traffic on the roads (and more serious crashes for the amount of drivers than there should be), drugs are a problem (mostly cannabis and P, not so much opiates), there can be gang violence depending on where you live. Books are expensive, food seems about the same, fuel is getting more expensive (it used to be noticeably cheaper, it’s well over $2/L now).
YANBU to plan to move here but do your research, choose your area wisely and get a job offer. Ideally, come over for a 6-8week trip to travel around and see which areas suit you. Whether it’ll work for you or not really depends on your reasons for wanting to.