Hello there,
I arrived in Melbourne at the beginning of this year, and I'm an analyst developer. I'm certain you would stand a good chance in Melbourne, as your skills are relevant (Java, .NET) and you have a decent amount of experience. I can't speak for Sydney though.
I willing to share my experience, but I don't have as much experience as you do and not with the same tech stack. I used to work for a big bank back home, and at the start had some troubles catching up. Back home companies adopted technologies slowly, while here they have moved to modern methodologies and technologies (think CI/CD, onion/ hexagonal architecture). After arriving here, I applied for at least 5 positions per week and didn't hear back a lot. This was tough, but I persevered and whenever I noticed a technology I didn't yet understand I spent my free time learning up. People expect customized cover letters to the position, but I don't know if it actually makes a difference. Also think about making your resume a bit more Australian (add an Australian address if you have one, format your phone number correctly, watch out with pictures, don't assume they know the companies).
After an arduous interview process, I ended up with a nice position with a technology forward company, although it was a step down it allows me to gain that 'local experience' and to master the new tech.
I had no luck applying for jobs from over-seas, which makes sense as things are a lot more face-to-face here and there is a lot of competition. If you get the opportunity, go to a MeetUp (.NET user group or Java community). There are always people around looking for employees, or willing to suggest you to their firm. Otherwise it's an excellent opportunity to network. Because we have to, not because we want to. ;-)