The military certainly does have mental health professionals who work with them. I'm not 100% sure of the exact nature of their service, whether they're reservists or personnel. I can certainly find that out for you. But certainly they do employ psychologists, psychiatrists, and other mental health workers to assist them.
I would imagine that like the rest of the Australian community, they are also having trouble recruiting some of the medical workforce in those areas, because of the general overall shortfall.
I couldn't actually comment specifically on defence, because I'm just not familiar enough with their situation and where they're up to in terms of recruiting.