Whilst they close at 10pm you really want to be there a bit before hand (it takes time to process the test), Brisbane processes the tests rather quickly but I'd show up around 8pm ish that way they can process it that night. My result even after queuing for a few hours came back about 30 minutes later so if you're lucky you'll get the result back before you even get back home.
There are normally a few evening flights around 9pm, 10pm and 11pm, Not all of them run each night so if you search on google flights the date and flights to Doha (DOH), Dubai (DXB) and Singapore (SIN) you'll be able to find.
Yeh it was bad, like he even whilst waiting decided to take his checked bag down stairs to security before he had checked in (those who've been through Brisbane would know what I mean), when I left he'd completed several laps of level 4 and then was onto level 2 the arrivals.
By doing the test the night before you can just stroll on up to check in, expect a temperature check at the start of the queue and then be prepared to show all documents at the desk - whilst not a requirement if you have them all printed it'll make both yours and the check in agents life 1000x easier.