The Global Employability University Survey 2014 has ANU as the top ranking Australian university (20 in the world), followed by Monash University (33), UNSW (55) and University of Melbourne (50).
This compares with the Times Higher Education World University Rankings 2014-2015 with the top Australian institution, University of Melbourne (33), then ANU (45), Sydney University (60), University of Queensland (65), Monash University (83), UNSW (109).
The university ranking system I find most interesting is Webometrics. This is based on an analysis of the university's web pages. With measures for presence, impact, openness and excellence. On these measures, Australia has first the University of Melbourne
(82), then University of New South Wales
(96), University of Queensland
(98), Australian National University
(101) and Monash University (114).