What one has here appears to be a "natural experiment," in that the researchers looked at when daylight saving time began as a policy in Australia. (It is already known to suicide researchers that seasonal variation in daylight length is a strong risk factor for suicide, resulting in seasonal variation in suicide rates.) The way to check this conclusion would be to look at other countries (or states in the United States) where policies on daylight saving time have changed over the years. This is not an ideally controlled experiment,

http://norvig.com/experiment-design.html

but suicide data are gathered by a standard World Health Organization methodology all over the world,

http://www.who.int/topics/suicide/en/

and when other national policies change in a country, or differ between countries, it can be useful to look at whether or not those policy differences make a difference in suicide rates. Sleep regulation is well known to be an effective treatment for mood disorders, so this is a plausible correlation to look at to see if there may be a causal relationship between the policy and the medical outcome.