As above you are mixing loyalty programs. They do not match.
What ffp's are you a member of now?
Frequent spending (for ff miles) is not the same as frequent flying.

Airlines that fly USA/Canada to/from Australia (not from all airports to all airports)
- United UA (LAX SFO – SYD MEL) [Star Alliance]
- American Airlines AA (LAX - SYD) [OneWorld Alliance] (AS partner)
- Qantas QF (LAX SFO JFK DFW HNL YVR*– SYD BNE MEL) [OneWorld Alliance] (AS partner) {* seasonal}
- Jetstar JQ (HNL – SYD BNE)
- Delta DL (LAX – SYD) (VA & AS partner) [Skyteam Alliance]
- Virgin Australia VA (LAX – SYD BNE) (DL partner)
- Hawaiian HA (HNL – SYD BNE via Hawaii) (AA & VA partner)
- Air New Zealand NZ (LAX SFO IAH YVR via AKL) [Star Alliance]
- Fiji Airways FJ (LAX via Fiji) (QF, AA & AS partner)
- Air Tahiti Nui TN (LAX last segments on codeshares) (AA & DL partner)
- Air Canada AC (YYR – SYD, BNE from Jun 2016) [Star Alliance]
And others via Asia & Middle East