Thanks for answering my question.
I think you need to analyze this in more detail. I don't mean here on MN, I mean at home, in peace and quiet, maybe with a pen and paper.
You're unhappy more than you are happy, connections are hard to make and family is far away. Ok. But why? What exactly is it that is making you unhappy? Why are the connections hard to make? Is it because you are a SAHM? Are the people unfriendly at your children's school so it's difficult to get to know other mums?
How old are the children? Lots of people have asked you that and you haven't answered the question for some reason.
Would you feel happier if you went back to work part time?
Would a move to another city or state help? Lots of people have asked where you are and you haven't answered, perhaps to protect your privacy, but I think it might help as others have experience of Australia and what different areas are like.
There's not much that can be done about your family being far away and that seems to be a major stumbling block obviously. But assume for one moment, that you decide to stay in Australia, (it's a thought experiment so don't immediately think "but I don't want to stay), what could you do to increase contact with family members? For example I used to play online games with family members with a chat function and that was a lot of fun.
You mention that you aren't happy with the education system in another post. Again, why? And how old are the children!! Is there anything you could change, such as moving the children to another school, getting tutors? Someone here might be able to help.
I've written a lot of questions here and don't expect any answers but I think you do need to go into more detail in your own head about what's wrong rather than the blanket "Don't like it, family's far away, want to go home" mode of thinking you are currently in.
Wish you all the best OP.