I went inside and got my trusty bird book - The Field Guide to the Birds of Australia by Graham Pizzey and Frank Knight - and discovered that the raptor was a peregrine falcon, Falco peregrinus.
It proved a little difficult to find a photo with the colouring of our local birds - their heads tend to be lighter coloured than many - so here's an illustration from Birds of Prey, Prang's Natural History Series for Children by Norman Allison Calkins, published in 1878, which is fairly close to it. A handsome fellow, don't you think?
I suppose I shouldn't have been surprised because there is ample habitat for falcons in the bushland surrounding the suburb where I live. Within a few minutes walk there are two golf courses with bush areas - one even has a resident mob of kangaroos - and two large expanses of bushland reserve with wetlands that would provide excellent hunting for a smallish raptor. The thing is we don't often see them away from the bushland so I guess this one must have worked out that doves are in plentiful supply here.
This video gives you some idea of the incredible speed a peregrine falcon can reach https://www.youtube.com/watch?v=j3mTPEuFcWk