Not sure about NZ, but Aus is merit-based for IMGs due to the internship shortage, which some say is intentional so they only get the best of the best. Or if you don't mind working in rural areas like Alice Springs or Pilbara. You can fight for a position in Sydney, Melbourne or Brisbane if your grades and CV are good enough or the dept head really likes you.

Having worked in both countries, I would say Aus is not much different from Singapore except Aus workload is better (possibly the best in the world that's why UK grads going to Aus in droves)/training time longer.