The Gravity Recovery and Climate Experiment (GRACE) twin-satellite gravimetry mission has been monitoring time-varying changes of the Earth's gravitational field on a near-global scale since 2002. One of the environmentally important signals to be detected is temporal variations induced by changes in the distribution of terrestrial water storage (i.e., hydrology). Since water is one of Australia's precious resources, it is logical to monitor its distribution, and GRACE offers one such opportunity. The second and fourth releases (referred to as RL02 and RL04) of the 'standard' monthly GRACE solutions with respect to their annual mean are analysed. When compared to rainfall data over the same time period, GRACE is shown to detect hydrological signals over Australia, with the RL04 data showing better results. However, the relatively small hydrological signal typical for much of Australia is obscured by deficiencies in the standard GRACE data processing and filtering methods. Spectral leakage of oceanic mass changes also still contaminates the small hydrological signals typical over land. It is therefore recommend that Australia-focussed reprocessing of GRACE data is needed for useful hydrological signals to be extracted. Naturally, this will have to be verified by independent 'in situ' external sources such as rainfall, soil moisture and groundwater borehole piezometer data over Australia.