The bird returned! Guess it is the same one. First saw it sitting in the Allocasuarina next to the bird bath, resting on one leg. It flew down to the bird bath, drank, then bathed in the water. When I walked outside, it flew up to one of the big eucalypts nearby. These photos show it to have a rounded tail (definitely not squared), so still wonder if it is a Brown Goshawk. Although the last photo does show it to have a longer middle toe, other photos don't seem to show such a difference. I am just confused about Identification of this bird - if it is the same one as I photographed the other day in the birdbath!
This big bird was sitting in our birdbath. It has been identified by Albert Golden as a Collared Sparrowhawk. He commented that the long middle toe and 'goggle' eyes identified it as such. It would have been sitting (as in the first photo) for at least 5 minutes while we were watching. It did look at me standing in the doorway with the camera, but appeared unperturbed. It then flew to a nearby tree (scattering little birds in all directions), then flew back to the birdbath, where it sat on the lip for another 5 minutes or thereabouts before flying away.