Crystal, do application for TR60 online via Sydney get pre-approval email then send paperwork to them. Very easy. I have done TR60, OA and now on OX all from Sydney consulate
you don't need a visa to do what you have said and when you come back into Thailand and get the 30 days exempt you can extend that for another 30 days if you want at the immigration office
Get a letter from her partner saying he accepts all financial responsibility for her whilst she is in Australia. See if that helps, I did it that way but it was years ago