Many children on TT flights in economy. Not considered a long flight: only about 3:30 ~ 4:00 hrs.
Depending on the aircraft it may have bassinet seats.
NZ Works delux is not business class - still economy class. QF business class can be $$$$
JQ Jetstar also fly WLG to the Gold Coast OOL (close to Brisbane)
https://en.wikipedia.org/wiki/Wellington_Airport