The pinnacle in terms of performance was after the 16 test streak, IMO. That was a remarkable team and performed brilliantly, but Australia's brutal dominance between 2000 and 2005 could have produced that sort of streak at any point.
The strongest side and the strongest performance for mine was the back to back series against South Africa in 2001/02, when Australia won 5 of the 6 tests. There were a couple of relatively weak points in the side, mainly Mark Waugh and Brett Lee/Andy Bichel, but the side overall was incredibly strong, and that top 7 has never been bettered at any point in test history IMO. South Africa were a very good outfit, but it was a thrashing. There are greater outright achievements than hammering South Africa, like winning in India, but that was the peak of the team IMO.
On the topic of Australia's period on top, one stat that always amazes me is the number of washouts. Since the 1-0 loss to Sri Lanka in 1999, Australia have played 26 test series excluding one-off tests and the one currently in progress. They've won 22 of those series, drawn 2 and lost 2. 12 of those 22 wins have been washouts. Seven 3 test series, four 2 test series and a 5-0 win against the West Indies.
By way of contrast, the West Indies didn't lose a test series between 1980 and 1995, playing 27 series of more than 1 test in that time. They drew 8 of those 27 series and won 19, but only two of the 19 wins were washouts, both 5-0 against England. It really shows how Australia have pushed for results and really dismantled opposition sides more than any other team in history, and how overstated the weakness in dead rubbers is compared to other dominant teams.