The four states covered here sit at three points on a line, from a preference to an instruction the law backs.
Queensland: signed instructions
Where a personal representative is arranging the disposal of the remains and knows the person “left signed instructions” to be cremated, they must make sure an application for permission to cremate is made and, if it is granted, that the person is cremated in accordance with those instructions.
The Act says in so many words that this overrides the common law, to the extent that it lets a person direct their personal representative to cremate them and qualifies the personal representative’s right to decide. The same signed instructions also switch off the rule that lets a spouse, adult child, parent or personal representative block a cremation by objecting.
South Australia: a will, or a signed and witnessed document
South Australia’s Law Handbook explains section 9(3) of the Burial and Cremation Act 2013 this way: an objection from the personal representative, a parent or a child stops a cremation, but not if the person directed cremation in their will or in another document they signed and had witnessed. The handbook adds that an executor named in a will is responsible for dealing with the body as the will directs.
New South Wales: the one firm line
A wish to be cremated is a preference the executor is not bound by; a wish not to be cremated must be followed. The application for permission to cremate asks whether the person left any written directions about how their remains should be dealt with, what they were, and whether the applicant is satisfied they were made “in a state of sound mind”.
Tasmania: a preference
Tasmania’s Public Trustee describes a will as a convenient place to record funeral wishes, and is clear that those wishes do not legally bind the family or the executor. If the family contacts the Public Trustee before the funeral, the family is told of any wishes set out in the will.

The timing problem
Whatever the law says, a will has to be read in time to matter. Cemeteries & Crematoria NSW notes that “typically a will is not made available until after the funeral.” Tasmania’s Public Trustee gives the same warning, and suggests making sure loved ones know your wishes in case the will is not reviewed until afterwards.
So it helps for the wish to live somewhere besides the will. Both bodies say the same thing in different words: tell the people who will be making the arrangements. Cemeteries & Crematoria NSW suggests recording your preferences and making sure your next of kin know where they are kept.
What a will can say about a funeral
Tasmania’s Public Trustee gives examples of funeral wishes a will can hold. In summary, they cover the big choice (burial or cremation, and where the body or ashes should rest or be scattered), the shape of the farewell (any religious requirements, music, and whether donations should go to a charity instead of flowers), and the money (how much should be spent, and how it is to be paid, for example from a prepaid funeral or funeral bond). It also mentions donating the body for medical purposes, and naming a preferred funeral director.
Victoria and Western Australia are not set out here. For those states, a lawyer there can say how a written wish is treated.