The only setback here is that you might have to work odd hours on weekends and holiday seasons.

The job of a cleaner is one of the highest paying part-time jobs in Australia

First of all, do you have a vehicle?
If yes, work as a delivery person.
If not, you can go for Cleaning.
But there are a lot of other high paying part time jobs in Australia that pay a lot more

Professors or other faculty in the specific field are usually the ones who do the hiring for GA positions-

The application process usually occurs a semester before the position begins, and students are hired based on their academic achievements, application materials, and faculty recommendations. The first step for preparation is research. Go to the specific college department’s website to find out what professors are actively doing in their fields. If you can find any information on the graduate assistantships the department offers, read through that too. And use it during the interview.

You can try for one of these part-time jobs for college students-

Tutoring - $13-25 per hour Bookkeeping - $15-20 per hour Data Entry - $10-15 per hour Freelance Writing - $20-25 per hour, Up to $50 per article

For more options, read this article

Doesn't hurt to apply

Dog walking might pay you more
If you decide to work in a relatively expensive area

A virtual recruiter is a liaison between an employer and a potential employee.
They contact several professionals and set up/conduct initial interviews between organizations and candidates.

Read more about it here.

You will really have to know about the history of the place
It's important to be well-read about it

See, that also depends on how much time you have, right
If you have more time and can accommodate a lot of freelance projects...that will earn you a lot
If you have less time, teach a limited number of students and charge a bit more as you get more and more credibility

You can use these portals to get your internship-
Virtual Internships
Intern Abroad HQ
Remote Internship

You can actually work full time during the summer (after being in the US for a year) and work part-time all year round.

Hey Manas,
There are primarily 2 different types of jobs that you can apply for when studying abroad. They are:

Off-Campus Jobs On-Campus Jobs
In USA, students are allowed to apply for curriculum related part-time jobs on-campus. Off campus jobs generally consist of jobs such as being a receptionist, waiter, etc. While examples of On-Campus jobs could be Library Monitor, Teaching Assistant, etc. When the college is not in session, most universities even allow students to work off-campus. There are several blogs that tell you super helpful stuff about part-time jobs for international students. Try reading these for more info-https://ischoolconnect.com/blog/part-time-jobs-for-international-students-in-the-usa/
https://ischoolconnect.com/blog/benefits-of-working-part-time-while-you-study-abroad/