Both daily AA flights DFW-NRT are D7 every day the week of July 7 (except the 12.05 pm on Monday July 7, which is D6), so no problem with availability there. Use an evp to upgrade to F.

The QF flight NRT-MEL only runs 3 days a week and is being cancelled begining early September. However, for your purposes, it's D9 on Monday July 7 and Thursday July 10 but D0 on Saturday July 12. You can't make the Monday flight unless you leave DFW on Sunday July 6. I'd fly Monday, spend 2 days in Tokyo and then the Thursday flight down to MEL. Alternatively, fly ex-DFW later in the week and connect direct (into NRT mid-afternoon, out at 8.20 pm)

Coming back - LAX-MEL the week of Sep 13 - D availability is a bit all over the place, both on QF and the AA codeshare, but it's there - just pick your day from what's available.