Fly AA to LAX or start there. Fly QF LAX-AKL in business (no first on that route), or QF LAX-SYD/MEL in first and then SYD/MEL-AKL in business (no first trans-tasman).
Cant upgrade on QF (only QFF points and upgrade credits), to get into business or first would need to buy the ticket or award in the desired class.