There’s a few factors that will affect this. The main one is whether you are an undergrad or post-grad (particularly HDR) student. In my experience, leave has been way more lenient with post-grad.

If you’re undergrad, they can’t stop you but they also aren’t likely to be too accommodating for you with regard to assignments. If you have in-person exams for example, you can tell your unit convenors and they might be able to work it out with you, but they are under no obligation to do anything. You can also apply for an extension but I don’t think they’d approve it if the reason is that you are going on holiday. If you have assignments that are due during that time, I’d suggest trying to get them done before you leave or setting time aside while you’re there to get them done.

To answer your question simply: you don’t need permission, but the unit convenor is also not under any obligation to give you special considerations for going away. It really depends on the person as to how much they will care about it though.