She does not have any power, her party has power collectively. A prime minister has no more power than any other minister. She's not like a president, she can't decree law.

NZ also has a constitution, the constitution is made up of multiple discreet documents including Te Tiriti O Waitangi, the founding document of New Zealand, the bill of rights act, the human rights act, the constitution act, etc.

The lack of a constitution is in some ways a good thing, democracy has to evolve as time evolves, some countries place too much of their identity in outdated laws which are 231 years old.