It must be a nightmare for lawyers if they move interstate with each State having its own law. At lease in GB we only have England and Wales laws and Jockland law.Agree completely; generally diminished responsibility is a matter for the defence to prove in a case of murder; it certainly is here in NSW. Not sure if that is the case in all states.
Each state has its own criminal laws. The NSW law is simple and very similar to the English law on which it is obviously based. Generally, there are three distinct intents that define murder; there are four separate intents that qualify as murder; the intent to commit GBH, the intent to kill, the reckless endangerment and the intent to commit a serious offence (usually one with >25 tariff) that leads to a death. Queensland has added more; I think there are 7.
WA defines three homicide offences: Wilful Murder, Murder and Manslaughter. Wilful Murder covers only for intent to kill. Diminished responsibility would apply as a defence to Wilful murder, reducing the offence to Murder. It might also reduce an offence of Murder to Manslaughter.