The qualifications you may need will depend on the type of education business or services you are providing. In addition, these requirements can differ depending on the state or territory in which you are conducting business.
Generally speaking, however, if you are going to be working closely with young students and children, you'll need to obtain a Working With Children Check.
Furthermore, you need to consider IP laws that apply to you, especially if you'll be reproducing content for educational purposes. In these cases, it's wise to include copyright disclaimers in your content and T&Cs for students to sign when they engage with your business.
If you're looking to become a teacher, you'll need to hold the relevant degree and other specific qualifications to teach in a certain area or at a certain level.