Welcome to the Wefugees community and thank you for your question.
In order to marry in Australia you need a valid visa. You will find extensive information about this topic following this link:
To me it seems to be one of the toughest regulations I've ever seen to obtain a visa. Your partner either needs to be an Australian citizen or to hold a permanent residence permit. I couldn't find out whether a residence permit issued for a refugee will be sufficient or not. Maybe you should get in contact with Australian officials to get valid information about this topic.
Also, using the calculator on the website above I found out that the total costs for the visa for you and your two children will be more than 10.000 Australian Dollars. It will be valid for 9 months. Afterwards you'll have to apply for a partner visa which will cost the same amount if you want to stay with your spouse in Australia.
I know that this sounds quite disencouraging, still I wish you all the best.