Gogga
1 week is enough to get around and say gday to all the operators in Darwin for sure. Though I doubt you will be offered a job in that time. It's hard to say really. If your multi is charter on either a chieftain or baron, then that will make a difference. Otherwise you may be looking at a single first. I know others are saying just move up to Darwin however I wouldn't be leaving your job if your currently flying unless you have a job offer, not with how slow it is at the moment. If your not flying then by all means drive up and make the move.
Depending on night and IR renewals you may be close to filling some contract requirements with Chartair or Katherine av. I don't know what they are exactly but could be worth looking at.
Hope that helps.