Dear Butterfly Kylie~
I'd like to join Sarah in saying how sad we are that you have not only the death to cope with but also the financial burden, and now threats for non-payment.
Each state does have some mechanism for help with "destitute funerals" payments however they do vary. Sarah's link does give some information on these.
Additionally Social Welfare Organizations such as Anglicare, St Vincents, Lifeline and others may be able to help as this is an emergency.
I'd suggest also you look to the Federal Government who among other things do provide some assistance but more importantly social workers to assist you sort it out and may refer you on to other organizations
I'm not hopeful you will get an immediate response due to the pressures of the virus, however applying there may be enough to stay any action by the funeral house.
Please let us know how you get on.