Yes you probably should withdraw your student visa application as you won't be needing it, but this should not have any impact on your entry into NZ.
Because you have Australian PR, you are essentially granted automatic residency in NZ by showing your passport/residency + arrival card.
The Immigration NZ site should have everything you need to know:
Australian citizens and permanent residents do not usually require a visa for travel to New Zealand, unless they are a person with significant character issues as described in Sections 15 and 16 of the Immigration Act 2009.
Provided they enter New Zealand on a valid passport, Australian citizens and permanent residents will normally be granted a resident visa at the airport to stay in New Zealand.
An application for a resident visa is deemed to be made by completing the “New Zealand Passenger Arrival Card” and giving this to an immigration officer together with a passport or travel document. Resident visas granted at the airport are electronic, meaning you will not be given a stamp or label in your passport.
This resident visa allows the holder to remain indefinitely in New Zealand, to study, and to work for any employer, but it will expire upon exit from New Zealand.
If you intend to stay in New Zealand long term, you may decide to apply for a permanent resident visa (PRV). If you plan to apply for a PRV, your resident visa must be endorsed with travel conditions to ensure that it does not expire when you leave New Zealand.