For small downloads, the LiDAR data seems to work fine. From the ELVIS portal, you can select a data set from DEM-S, DEM-H, LiDAR 5m and LiDAR 25m. I only was able to get TransDEM to accept files in the ESRI format, with the MGA94 coordinate system (apparently within a meter of being WGS84 and therefore close enough for the accuracy involved).
You can access the portal here:
http://www.ga.gov.au/elvis/While a small area worked fine for the LiDAR data, I found that downloading the high resolution data for the area I wanted did not work with TransDEM. Possibly too big a filesize? It was around 160 MB. For now Im working out the tool, following the tutorials... but the small bit of LiDAR data looked like its something I want if at all possible. Is it possible to overlap/merge DEM files the same way raster maps are?