The clue to Kiaora's success is that her fiance is a New Zealander and, because of that, she managed to get a WP without a job offer. You would need a job offer to apply for a WP but I don't understand what you mean above by 'work permit under the Family Stream'. Do you have someone already in NZ who will sponsor you? I assume your partner isn't a kiwi if she has to apply for visas.
If you are allowed to apply for another visa, it would be preferable if your partner is living with you because then you wouldn't have the problem of not having lived together for 12+ months as is required. That only applies if you have been living together for 12+ months, of course
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You can use any of these to prove your relationship.
Evidence about whether the partnership is genuine and stable* may include but is not limited to, original or certified copies of documents and any other information such as:
a marriage certificate for the parties;
a civil union certificate for the parties;
birth certificates of any children of the parties;
evidence of communication between the parties;
photographs of the parties together;
documents indicating public recognition of the partnership;
evidence of the parties being committed to each other both emotionally and exclusively such as evidence of:
joint decision making and plans together
sharing of parental obligations
sharing of household activities
sharing of companionship/spare time
sharing of leisure and social activities
presentation by the parties to outsiders as a couple.
evidence of being financially interdependent such as evidence of
shared income
joint bank accounts operated reasonably frequently over a reasonable time
joint assets
joint liabilities such as loans or credit to purchase real estate, cars, major home appliances
joint utilities accounts (electricity, gas, water, telephone)
mutually agreed financial arrangements.