Those temporary powers mentioned there include forcing people not to gather in public places (I would assume this would include churches as well), the creation of mass graves (if required I guess) and the ability to quarantine infected individuals and (probably) enforce treatment on them. At the moment I'm not sure on the probability that H5N1 will reach New Zealand, but it has been detected in Scotland recently, which appears to have provided the impetus for our government to propose these law changes.
Legislation giving the government the power to close New Zealand's borders in the event of an influenza pandemic has been introduced in parliament.
The bill adds influenza to the list of diseases that can be quarantined - along with cholera and yellow fever - and allows the Prime Minister to activate temporary powers to manage a pandemic.
It comes into effect in august but may be fast-tracked depending on how the situation develops.