I'm not sure how it works with a WHV, but I know for a Skilled Migrant visa application, that you will be required at some point to produce a signed employment contract, along with cancelled cheques and bank statements to show that you've been getting paid. Having an employment contract up-front can also tremendously speed-up the visa application process.
In your case, I wonder if you might be able to arrange for your employer to pay you an amount that you would then pay back as rent, through a rental agreement that was separate from the employment contract. As long as the amount met minimum wage standards, it seems like that might be a viable approach. However, your employer will also need to withhold and report employment taxes (PAYE) -- at least for the 3 month work period required by the skilled migrant program.
In addition to NZIS, you might also consider talking to a solicitor and/or an accountant about your options.
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