There is a massive shortage of GA instructors in Darwin at the moment. I'm not too sure how many jobs are available for fresh (less than 300HR) CPL pilots to be honest as i haven't asked around. I agree with the other posts, the only thing to do is make an appearance face to face at the many GA operators and dont let their desk girl turn you away. Can I suggest also don't keep a narrow mind with the "Darwin Darwin Darwin' approach like a lot of others. There's a good GA presence in Katherine and Alice Springs etc etc,. If your willing to keep and open mind and do the hard yards as a glassy or something first up here you will be sure to get success eventually.
Maybe its worth a look here?
Jobs in Northern Territory - Gumtree Australia