If the visa you're going to get is for more than six months, you can immediately sponsor your partner for a partner-sponsored work visa.
If your child is of school age, you have to get her a student visa, and if she's below school age, then a visitor visa. You apply for your wife's and child's visas at the same time as your own, with a covering letter linking them, then they'll be worked as one case, with the CO supplying things you won't know to start with, like your visa number, as they become available, and your wife and child's visas will match your for time. (Also, supposing you're having to get your child a visitor's visa, there won't then be the potential for odd questions about when she is leaving NZ, with whom, etc..)