Thanks for the quick input. A couple of thoughts.
1. I looked into AA's programs. Any thoughts on whether it matters which OneWorld airline I join with? I used to have Gold on BA years ago back when I lived in Europe. I've never had a particularly good experience with AA, hence the reluctance to get too tied up with them (are they better internationally than US domestic where I've found them to be dreadful?).
2. Diamond is Delta's absolute highest level (unless there's some secret even higher level that I'm not aware of) and requires 125k miles to qualify. Nonetheless, it doesn't appear to matter if QF is unwilling to match.