What exactly are you referring to by "teaching"? Are you wanting to teach at a school while you're completing your university degree? This will likely not be possible. Of course, as mentioned above, if you are referring to tutoring, then it is definitely a great way of earning some money while studying and may not be as demanding as other regular casual jobs.
Depending on the university you attend, you may also be able to participate in peer-assisted study sessions (otherwise known as PASS). PASS facilitators are employed to facilitate group study sessions for their peers at university and generally require you to achieve high marks in the subject(s) for which you wish to become a PASS facilitator. The possible benefits of being a PASS facilitator include:
Paid employment on campus
Improved communication and public speaking skills
Opportunity to network with professional and academic staff
Development of leadership and teamwork skills, particularly through working with a team of like-minded peers.
Potential access to professional development opportunities
Several universities offer such programs, including:
No worries! Keep in mind that in order to work in a NSW school, you will be required to gain accreditation from NESA. If you wish to become a teacher, you will need to firstly apply for Conditional accreditation, provided you satisfy one of the following conditions:
you are in your final year of an accredited undergraduate or graduate entry teaching degree
you have completed a non-teaching bachelor degree (such as a Bachelor of Arts) and have an offer of employment as a teacher in a NSW school.