Does Brisbane have hawks? actual serious question cause a hawk or some kind of bird of prey flew into my backyard right at the start of the covid period. I back onto a creek and a bit of bushland. It sat on the fence for a short while then flew off.
In short, yes Brisbane has raptors, and almost certainly has hawk species as well.
Hawks (and other raptors) are ubiquitous across Australia and everywhere else in the world except Antarctica.
As T-Boon was alluding too the only species that have been reported to display "firehawk" behaviour are the Black Kite, Whistling Kite, and Brown Falcon, in other words none of the firehawk species are actually hawks.
All three species are found across Australia, PNG, and some other islands in the Pacific, though the Black Kite's range extends across Asia and Africa as well (though it's never been reported firehawking outside of Australia). All of them are also found in SEQ, so there's a chance that the raptor you saw was one of them.