Natalia, I say go for it. It is strange - you are a single woman wanting a child and yet your motices are questioned, but I often see posts on this site with women who are (IMO) very young expressing a desire to have children and getting heaps of messages of support, or women who are in shaky relationships who want kids and get told that if they want to have a baby they should go for it. Yes it is ideal to be in a long term supportive relationship, etc etc but not everyone has that.
As far as I am aware IVF is an option for single women in NSW, but you would have to check with a local clinic.