Hi Saso and welcome.
If you have the right skills, qualifications and work experience to apply for permanent residency or a work permit, you would be able to take your family to NZ. But, firstly, you need to decide how you are going to get into NZ long term. By that I mean which visa category you hope to apply under. Getting a job offer is a very good start, but you will need relevant qualifications and job experience as well before you can apply for a visa.
Have you looked at the
NZ immigration website yet? It's a good place to start.
I don't think it would be easy to find a job in NZ fast, especially when you aren't already in the country. Some people have managed to get jobs but many others have had to travel to NZ to meet face to face with potential employers before they have been able to get a job offer.