I think these answers will show you where you need to look to find out more detail of the regulations. As I don't know all the details of your situation, you should check yourself - don't just necessarily believe what I
think may be true.
You need to look at SM7.10, quoted in my next answer. If your job comes in Part C of that list, you have to have 3 years' experience.
If your job is classified as '351411 Cook' for your application, that comes in Part C of Appendix 6 of the INZ operational manual
http://www.immigration.govt.nz/opsmanual/35165.htm. It looks as though, according to SM7.10
http://www.immigration.govt.nz/opsmanual/46411.htm, your qualification would cancel out the need for the minimum wage they mention, BUT you need three years' experience.
If your wife's hepatitis B is 'surface antigen positive and meeting criteria for anti-viral treatment in New Zealand', then it is going to cause at least delays, and probably, problems.
http://www.immigration.govt.nz/opsmanual/45634.htm In any case, her medical is sure to be referred to the MA, and they will want reports and test results from her doctors. It is quite likely that you will be told she has to apply for a medical waiver, and the regulations say that, as your partner, if you are found to be eligible for Residence, she may be considered for that waiver as long as there is nothing else serious wrong with her.
http://www.immigration.govt.nz/opsmanual/45636.htm