Sorry to hear your news.
Just wanted to wish you all the best for whatever decision to come to. As people have said if you want to stay why not give it a go, don't let the single parent aspect get in the way of living your dream if Oz is where you want to be. It's not easy being here by yourself but i'm sure you have a great network of people here already for support. Afraid i can't advise on things you get as a single parent as only on a temp visa,the main bit's i'm aware of are the rent assistance and family tax benefit part A & B which you prob already know about (been looking a bit for the future lol).
Good luck Clare.x