You might want to state which DTV route you are applying for. In some cases a brief cover letter can summarize the purpose/direction of the application.
Residence certificate is obtained from the immigration office serving your area. You'll need to ensure a TM30 has been filed for you where you stay. You can pay a fee to have it quicker, otherwise it's a couple weeks
rule of thumb in Thailand. Embassies know nothing about immigration policies, and immigration doesn't know anything about ministry of foreign affair embassy policies.
You apply and get approved first, then she applies using your DTV visa number/approval for dependant reference. Use her Aus passport and some documentation of your current location and attest to such as well as attest to provide sponsorship for the child. Just write a brief cover letter for her application.