I didn't believe there were any faults around this area, or any apparent risk factors for strong earthquakes. Is the strength and number of these earthquakes normal normal, or is something odd happening here?
Actually, there is a shear zone in NW Australia. The Australian plate is somewhat stuck near the Timor Trough but keeps subducting in the west near Java. This naturally cause shear stress to accumulate in NW Australia which has to be eventually released as strike slip earthquakes.
See Whitney et al. for more details.
Are you confusing faults with tectonic plate boundaries?
Australia is in the middle of a tectonic plate, but there are countless faults within the plate, as within all the other plates. Each plate is stressed & eventually rock adjacent to some faults moves resulting in a intraplate earthquakes.
As the Geoscience Australia website states:
Although Australia is not on the edge of a plate, the continent experiences earthquakes because the Indo-Australian plate is being pushed north and is colliding with the Eurasian, Philippine and Pacific plates. This causes the build up of mainly compressive stress in the interior of the Indo-Australian plate which is released during earthquakes.
Broome is not all that far away from a plate margin. About 300 miles north of Broome the Australian plate is slipping beneath the Eurasian plate, and this is most likely what is causing the earthquakes. Aftershocks are common after earthquakes, so this is probably what causes the cluster. If such earthquakes are vey infrequent near Broome, that is perhaps because the Australian plate is moving very slowly. Friction sometimes halts it in places and tension builds up as it I tries to move forward but is prevented. When the friction is no longer enough, something gives, and that part of the plate lurches forward again.