Is this series of earthquakes near Broome, Australia normal?
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 &amp; 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.