Nothing wrong with Australian degrees per se, but the perception of employers (i.e. Singapore law practices) is everything.

The general perception of Aussie law degrees in Singapore is not favourable at all. MinLaw did Aussie grads no favours in 2015 by delisting 8 of 19 UK universities on "quality control" grounds yet increasing the number of scheduled Australian law schools, including certain institutions with LLBs not worth the paper they are printed on. It is no secret that we were arm-twisted into doing this as part of a certain FTA. The SG authorities didn't push-back too hard as they knew full well that the private sector would still of course filter out these graduates, but not before allowing the hapless (and often less academically able) students to spend colossal sums of money to graduate from such institutions before realising that nobody will hire them, even if their degree is from a "scheduled" university.

The top 3 or so Australian universities are still properly decent and can rival that of some UK universities. But how many employers will take the time to educate themselves on these matters? With the glut of SG/UK graduates, they don't even have a need to do so.

That said, you are right that many international firms do actually hire Australian graduates. But even without the bias often shown by Singapore firms, you are at best on equal footing with about 5,000 applicants from other SG/UK etc law schools trying to get in. What do you think are your chances?