The airline is going to check Timatic, a worldwide database of travel document requirements, when you check in, to ensure that your documents are sufficient for the countries you will travel to.
When they look you up, they will see, among a lot of other information, the following:
Visa required, except for Nationals of New Zealand with a
biometric passport (with an electronic chip symbol on the
cover) and an Electronic System for Travel Authorization
(ESTA). They must travel as a tourist, on business or in
transit, for a maximum stay of 90 days. (SEE NOTE 60190)
NOTE 60190: Passengers must have a return/onward ticket.
If they keep looking, they'll see the following in the Additional Information section:
- A return/onward ticket (or electronic ticket record) must
be to a final destination country other than Canada, Mexico
or contiguous (adjacent) countries or territories situated
in or bordering the Caribbean Sea. If a
passenger holds proof of residence in Canada, Mexico or a
contiguous (adjacent) country or territory and is
transiting the USA to that country or territory, then an
onward/return ticket to that country or territory is
So if the check-in agent is on the ball, they will ask for you to provide either Canadian residence or an onward ticket from Canada. If they aren't paying much attention, because travel to the USA is so common, they might not ask, but you probably shouldn't count on this.
As for clearing US immigration, the actual regulations state that onward travel terminating in Canada, Mexico or the Caribbean is not sufficient unless the traveler is resident in that country.
Applicants must arrive on a carrier that is signatory to a Visa Waiver Pilot Program Agreement and at the time of arrival must have a round trip ticket that will transport the traveler out of the United States to any other foreign port or place as long as the trip does not terminate in contiguous territory or an adjacent island; except that the round trip ticket may transport the traveler to contiguous territory or an adjacent island, if the traveler is a resident of the country of destination.
In practice, you're not likely to be asked about this, and even if you are asked, you are still likely to be OK. You'll most likely end up using a kiosk and having only the briefest conversation with an actual immigration officer.
If you have a temporary resident visa for Canada, such as a student or work visa, (as you plan to stay longer than three months, it sounds like you might do) then you are certainly OK as that will allow you to qualify for the noted exception. You'll show it to the airline to prove you have residence in Canada, and to the CBP officer if asked for it.