I heard about this recently, so naturally I'm interested as a kiwi.
New Zealand didn't declare war 6 hours early. It declared war alongside (or slightly after) the UK.
Officially, New Zealand’s declaration of war was simultaneous with Britain’s, at the expiry of the British government’s ultimatum to Germany to withdraw from Poland (9.30 p.m. New Zealand Standard Time, 11 a.m. British Summer Time). In fact, ministers and senior officials waited for formal advice of the expiry of the ultimatum, and Britain’s declaration of war on Germany, before taking action. It was not until 11.30 p.m. that the acting prime minister, Peter Fraser, issued a statement confirming that New Zealand was at war.
Source (NZ Ministry for Culture and Heritage).