Assuming that you each meet the conditions for the visa you're applying for, then it is normal to be able to travel at the same time.
You will need to find out what kind of work visa you can be eligible for. There is a general list here.
https://www.immigration.govt.nz/new-...all-work-visas But you are quite likely to be aiming for an Accredited Employer Work Visa
https://www.immigration.govt.nz/new-...oyer-work-visa, depending on your qualifications, and then getting a job offer. As you will see on that page, with the right conditions, you can support your partner for a Partner of a Worker Work Visa.
https://www.immigration.govt.nz/new-...ers#sc_0kJE6DR
When you have prepared all your evidence (details of what is required are on those INZ pages, and you will find more if you do a search on this forum), you can submit the two applications at the same time, noting that they are linked because you are a couple, then they will usually be processed by the same CO, supplying information you don't know at first (visa number etc.) as it becomes available. Of course, your partner's application will not be granted, even if all the evidence checks out, until and unless yours is approved first (because the partner's visa depends on the worker's visa).