Blue-spotted Hawkers are large dragonflies more often seen on the wing than resting. If you can get a good look at them while they are flying over still water, you can recognize them by the two distinct transverse stripes on the sides of the synthorax. Some of the Darners (Telephlebiidae) also have transverse stripes on their synthoraxes but do not usually fly over still water. I have sometimes seen, on partly cloudy days, Blue-spotted Hawkers hanging on fences, grass or trees.
This immature male blue-spotted Hawker has not developed the blue spots yet. Note the angled hind wing bases and the narrow 3-celled anal triangle circled in red.
Notice the rounded wing bases of this female Blue-spotted Hawker at Deer Vale NSW on January 16th 2013.
The male and female blue-spotted Hawkers differ in the shape of their wing bases which are angular in the male and rounded in the female. Abdominal segment 3 is much more narrowed in the male than the female as well.
All the Blue-spotted Hawkers I have seen laying eggs have not been accompanied by males.