I may be wrong.
For you, as a QF Elite, silver, if the flight comes in late I would hope that QF would assist with connections, if they have been asked to link the pnr's.
Phone QF & ask them to link your tickets.
When you check in, ask them to link your tickets.
When you check in, ask them to tag your bags to your final destination.
Of course you have to collect, clear, & re-drop.
It's always good nowadays (in the past 4 or so months), to have extra time up your sleeve.
Be pleasant, ask nicely. Dress well. Be the person you'd want to help out...
Also be aware that you may have been the one to have stuffed up with tight connections. Again, be pleasant, ask nicely ...
Might be worthwhile changing your AA connection to F, if at all possible. If not, be pleasant, .......