Look, if you have to make your case fit the parameters for sole parental responsibility, then you don't have a case for sole parental responsibility. Sole parental responsibility is only granted where one parent poses an unacceptable risk of harm to the child, or shared parental responsibility is not in the best interests of the child, so you're going to need evidence above and beyond just your word to successfully rebut shared parental responsibility. Has dad ever been charged with a violent crime? Has DHS ever been called for the child's welfare? Are there police reports? An IVO? Etc?
If the answer is no, then you don't have a case for sole parental responsibility.
As a word of warning, parents who seek sole parental responsibility with nothing other than their word as evidence of risk, can and often have wound up with an order reversing residency of a child.
Just because dad said he will fight for primary care of the kid, does not mean this automatically becomes a fight for parental responsibility. He's going to be told the same thing as you: that unless he can prove you pose a risk to the child, that's he's going to end up with an order for shared parental responsibility.
Children benefit from having both parents in their life, that's a presumption in law, and they benefit even more of their parents can put their issues aside and get along for the sake of their kid.
My suggestion is to contact Relationshops australia for two reasons - first to organise mediation to talk about care arrangements for the kid, second to enrol in a post-separation parenting course.
