Almost forgot about this one...

As it worked out, the guy sitting in front of me on the QR flight was doing the same thing, he was on my same QF flight ADL-MEL (in coach), so we went through the process together. He was flying QR LHR-DOH-ADL, and he also said that QR had less expensive business fares into ADL than elsewhere in Australia.

From QR aircraft through Australian immigration and customs (even with a checked bag) we made it out into the airport in about 15 minutes. They were funneling everyone to the e-gates, and that worked well for me, and my bag was one of the first out. The overall immigration and customs experience at ADL was similar to what I experienced at AUS (I prefer using secondary ports of entry when I can).
We asked about getting on the earlier QF flight (it was due to leave ADL at about 6:20pm), but it was oversold (we would have had plenty of time).
Our flight (7:20pm) wad delayed and left at about 8:15pm. Had no issues at all, spent some time in the Qantas lounge, which was surprisingly large for the city and airport (I'd compare ADL similar size as AUS but the QF lounge was probably 5x or even larger than the size of the AA lounge at AUS).

I'd definitely do this routing again if the price was right.