Should I become an elementary teacher in New Zealand instead of Canada since there are no jobs here?

What makes you think there are jobs for elementary ed teachers in NZ that Kiwis cannot fill? A lot of Kiwis have to leave NZ to find work. It's a small country. And generally speaking, public schools cannot sponsor foreigners for employment visas. You'd need a way to immigrate, then look for scarce work. Instead of elem ed, do you have the ability to major in science or math, then get your teaching credentials? The only demand for school teachers most places is for science & math teachers, especially those who can teach the more advanced courses. And school teacher as an immigration qualification is unlikely, too. Try the more remote, less developed countries if you want to be a school teacher, especially elementary level, though experience would be required, not just school & certification.

There are many teaching jobs in Canada, you just need to know where to look, and be qualified well enough to work those jobs. Also, are you wanting to teach in primary or secondary? If secondary then you shouldn't have trouble if you pick an in-demand subject such as French, Math, Chemistry, or Physics. If Primary then you'd be best if you were fluently bilingual and had experience. If you went abroad for a few years you could go to a place like Korea or Japan to teach ESL where you get free housing and airfare, a big paycheck and a huge potential to save along with experience. You could also take what is called a working holiday to NZ or Australia (or the UK, Ireland, and a few other countries) for a year to teach there, and then come back to Canada with experience. My son is a teacher of math and French. When he got his BE from Trent University in Peterborough, Ontario he went to Korea to teach for a year where he saved up a bunch of money and payed off quite a bit of debt. He went to Japan after that and then he went to the UK for two years. He now teaches in Belleville, Ontario.

Got to go where the work is.