Ambient noise tomography has been widely applied in seismic studies to invert for crustal and upper mantle structure, but has limited resolution for the near surface layer. A recent method involves measuring the ellipticity or ZH ratio of Rayleigh waves to further constrain shallow sedimentary structure. We apply this method to South-East Australia, using multicomponent ambient noise data obtained from the WOMBAT array. We present a shear wave velocity model, derived from the joint inversion of Rayleigh wave ZH ratio and phase velocities measured at short periods (2-10s). At shallow depth, our shear wave velocity model showed strong spatial correlation with the known surface geology. High velocities were associated with the Gawler craton and the eastern subprovince of the Lachlan Orogen. This contrasted with anomalously low velocities featured prominently in the locations of the Central Murray basin, Sydney Basin and the Northern Curnamona province at 1km depth. A low velocity, shallow layer of 0.5-2km thickness was detectable across study region, which was found to be thicker beneath sedimentary basins. We evaluate the strengths and limitations of the ZH ratio method for the South-East Australia dataset.