I want to eventually migrate to New Zealand, what college course should I take?

I from the Philippines and I plan to eventually migrate to Auckland New Zealand to live with my brother. However I'm worried that my current degree (business management) is not in demand in New Zealand, plus I don't enjoy working the jobs connected with my course. So I plan to eventually get either a second degree or a masters degree that will eventually allow me to migrate to NZL. I was planning on either getting a degree in Elementary Mathematics or Early Childhood Education, then working for 2-3 years before trying my luck in finding a job in Auckland. Will this be enough or do I need to search for another path? (I don't want to be a nurse or an accountant) By the way please don't send me a link to New Zealand's immigration site as I've already been through it a number of times