The department website says that Carers who are in receipt of Carers Allowance, Carers Benefit or DCA on 1st Thursday will automatically receive the payment. So if you are in the period where you are getting either the allowance or benefit after the death of the caree then you will get the Carers Support Grant.
I get it every year as I receive DCA for a child. I do not think I am entitled to it under the legislation as I work more than 15 hours per week. But every time I bring it to their attention I am told "the system says you get it".