To Q&A site visitors:
Below is a response from a lawyer in our networks, based on further information provided by the asker of this question via email.
"The Births, Deaths & Marriages Registration Act provides:
24 Change of name by registration
A person's name may be changed by registration of the change under this Part.
25 Application to register change of adult's name
(1) An adult person—
(a) who is domiciled or ordinarily resident in the State; or
(b) whose birth is registered in the State—
may apply to the Registrar, in a form approved by the Registrar, for registration of a change of the person's name.
(2) An application for registration of a change of name must be accompanied by the prescribed fee.
And:
28 Registration of change of name
(1) Before registering a change of name under this Part, the Registrar may require the applicant to provide evidence to establish to the Registrar's satisfaction—
(a) the identity and age of the person whose name is to be changed; and
(b) that the change of name is not sought for a fraudulent or other improper purpose…
Hence the Registry asking about the default of debt to satisfy s28(1)(b) above.
In my view, you must disclose the existence of the debt to avoid an allegation of perjury. However, you should take with you to the Registry any documents you have from bank or counsellor or otherwise that show your incapacity to pay and the non-pursuit of the debt by the lender. As you are on Centrelink benefits, my understanding is that you cannot be pursued in bankruptcy proceedings but your financial counsellor would advise you further on this.
You should also take your pension card and any letters you have from your doctor, psychiatrist or the Gender Dysphoria Clinic (Monash) attesting to your diagnosis of GID and stating your need to be identified as female. If you have employed your female name in common usage (repute), you are also legally entitled to be recognised by that name.
30 Change of name may still be established by repute or usage
This Part does not prevent a change of name by repute or usage.
If you can demonstrate that this is the case by producing letters, accounts, utility contracts in this name, take them with you as well.
The people at the Registry are generally well briefed and able to deal with your issue sensitively. If you have any issues, let the Q&A site administrator know and the details will be considered.
Good luck."