I'm a MH Nurse working for Country Health although I am based in Adelaide (Glenside Campus). I've been working in Adelaide for 5 yrs. First got my job (at James Nash forensic services) whilst in the UK via an agency (Geneva Health based in New Zealand). Since then I moved south and worked at Noarlunga Mental health services and now work on an emergency MH phone service.
Basically within the state for government there is Central and Northern Local Health Network which encompasses mental health wards at Queen Elizabeth Hospital, Royal Adelaide Hospital, Glenside Campus, Modbury Hospital and Lyell McEwin Hospital. Then there is Southern Mental Health Local Health Network which encompasses Flinders hospital (Margaret Tobin Unit) and Noarlunga Hospital. Then there is Country Health which has one ward on Glenside campus for patients from the rest of the state (although they are about to open regional centres in Port Augusta, Port Lincoln, Berri and Whyalla I think - these are all far to far away to commute to but interestingly some of the hold up's with opening the new units will be difficulty recruiting to country positions).
In my opinion you are much more likely to gain a position as a new graduate on one of the metropolitan or country mental health wards than working in community teams which require more experience and knowledge of the mental health act etc. However there is an abundance of mental health community teams and emergency services which will sometimes take new graduates. In the past few years there has been a move to open 'step down' units generally called Intermediate care centres or community recovery centres. Within twenty mins drive of Flagstaff you have two options in these areas The Southern Intermediate Care Centre located on Noarlunga Hospital grounds or the Trevor Parry Community Recovery Centre across the road. As these are newer services, (again in my opinion) there are a bit more progressive and are more likely to welcome a new graduate in the hope that your practice is more up to date and recovery focussed. Otherwise you could try the Margaret Tobin Centre based at Flinders Hospital (15 mins from Flaggy) which has 3 mental health wards from memory 5K, 5H, 5J.
In terms of the job situation, there is always a shortage of mental health nurses. Sometimes this is hidden by not advertising so much and using more agency nurses dependent on the political situation at the time and I suspect we are in this sort of scenario at the moment.
Oh - Your other options are private hospitals of which there are two in the state both based in Adelaide - Fullarton Private and the Adelaide Clinic.
Hope that helps. Good luck with it. Shout if you need anything else.