What type of short-term visa should my Thai partner apply for to visit Australia with me?

A tourism visa is what she'd be seeking. The application is done online. What will be required is

(1) Statement of employment from her employer, stating years of service and salary

(2) Bank statements from previous 12 months

(3) Any land/property ownership documents

(4) Immediate family details

I do it every year for my lady. The first is probably the hardest, but with a good record of non-overstay it gets easier. In the last few years she's also had visas for UK three times and Schengen twice

Application is started here

Ask in a Australian visa group, they know about Australian vica.

Here the knowledge is about visa for Thailand.

There is a group for Australians in Thailand that might be more helpful - I’m not sure of the exact name

The & More part is imo still about Thailand.