Hi (first time posting in flyertalk, love this site!),
I did a similar move last year, two years time in Melbourne after living in NY. I would also recommend AA while considering a few things:
1) I started with Qantas as we get lounge access and preferred prices through our company. Had no status with AA at the time. Qantas is fantastic in regards to customer support, flying experience, lounge quality, etc. Night and day compared to most of my experiences state side (literally unable to reach a person at US Airways via phone for over two years; could also legally justify murder due to insanity for half the Delta people I've interacted with; United in Newark - geez...).
Lounge access isn't that expensive though, and find that it's best value is international. Domestic lounges can get quite crowded, even though they are big, as it seems the whole country has access.
2) It is really easy to gain access to elite levels with Qantas due to their minimum points and qualifying status credits. I've rapidly accelerated to elite status (Gold, then Platinum) in under a year. While flying internally in Oz it is accessible everywhere, and of course has the oneworld alliance. They have great tools for estimating points earnings, redemption options, etc. I play with them all the time before making bookings.
3) Redemption benefits are terrible for the Qantas program. The value of points are likly 75% the value of AA points. When redeeming for flights you get hit hard twice, first in the overall number of points required for redemption, second in the taxes and fees still required on top of it. As an example, the "where could I go" section estimates that to fly round trip from Melbourne to London would require the following:
Economy: 128k points, AUD $939 in taxes, fees, and carrier charges
Premium Economy: 192k points, AUD $1331 in taxes, fees, and carrier charges
Business Class: 256k points, AUD $1642 in taxes, fees, and carrier charges
First Class: 384k points, AUD $1642 in taxes, fees, and carrier charges
The taxes and fees really bother me. For work I was quoted a $700 round trip economy flight between MEL
& SIN, ~250 for tickets and ~450 for taxes and fees. The other redemption go from a little worse (e.g. upgrades) to throwing away points (Qantas store).
From what I can tell (sorry don't have research readily accessible), AA is lower in points for redemption, much lower in fees, but will also have a bit lower earning rates. Check the AA site, most flights will have 100-150% miles flown earnings.
4) Do consider how you will be earning, in what time frame, and what your current status with AA is. Since it can be relatively quick to elite status with Qantas, if you build up elite within a year you can that try a status challenge with AA to minimize the pain of starting from scratch or not getting to a higher elite level. So if you get Qantas platinum, switch to AA gold, you can potentially get to AA exec platinum faster while getting elite oneworld benefits in the mean time. I'll be making the transfer to a challenge after the June 16th date to extend the AA status through Feb 2017. Check out other forum and blogger comments on AA challenge to learn more.
If the CC option is a good one to get points and status at AA, just jump on it from the start. Also keep in mind transfer partners for AA, such as SPG at 1:1. Qantas doesn't appear on most of these programs. Even my corporate Australian AMEX doesn't have Qantas as a partner.