There are few options for animation and related courses in NZ:
1) Natcol has animation and advanced 3D courses which are good.
2) Media Design School has animation courses.
3) Design & Arts College has fine arts, architecture but no animation.

The first two options are good for animation.

Visual effects courses are available in Media Design School www.mediadesign.school.nz/
This school has a good lab facilities and infrastructure.

- CTUBuddy

Visual effects is a highly specialized field in the entire creative industry. The skills are required more in movie and animation industry. But if you consider graphic design that is more generic (relatively). Graduate from this can find jobs in any industry like print, digital media, animation, movie etc.

Obviously visual effects jobs may be less compared to graphic design but they may be paid more because of the shortage too.
Animation and movie industry is big in Canada compared to New Zealand. Hence visual effects could be a good choice in Canada if you want to consider that possibility.