Only when you board the aircraft its when you have to show either the small slip of thermal printer printed paper that gate spat out, or that you show on your mobile device the QR code... or a home printed BP.
But other than that, no, QF does not do a match.
If you have sat at the seats near gates though, you will note that the printer does print out rolls and rolls of fax like paper, that has got names on it, so QF know who has and who hasn't checked in.
In 20 odd years of flying QFd, I have only been asked to show id if and when things go pear shaped, and I have to go to the girl/guy standing near the check yourself in counters at the domestic terminals, so sometimes, its good to carry photo id for Au domestic flights.
What ever, but just take a long your DL if you have it, just in case you need to print out a BP for any reason at the airport.
Imagine this scenario, a lady on "don't fly JQ" website, related this: she didn't realise that her return flight from CNS to MEL (if I am not mistaken) would depart from the international terminal, orange sticker sort of thing... some of us can always dream that we are told, you have to go to the international terminal, as you have been put onto a JQi flight...