Father on birth certificate?

Has anyone had success about not having the father on the birth certificate?

I’m from Australia. And my baby’s father has not been supportive of the pregnancy. He didn’t go to appointments, he didn’t care for the baby’s health during the pregnancy nor mine as he tried cheating multiple times with different woman putting us at risk of STDs. He has not provided a cent for this baby, like he has not bought one thing or paid for any appointments. I have been the sole provider of all necessities and have been the sole carer for her. She lives with me and my parents. And I have invited him to see her multiple times but he more times than not, chosen to see his friends/party. And now he’s getting angry on the phone to me because he can’t see her because our country is pretty much in lockdown because of Covid19 ( he hasn’t been isolating and has been partying with friends). He believes he should be able to come to my house any time to see the baby, regardless of whether it suits me or is safe to do so (covid 19) Baby is 7 weeks and he hasn’t provided any form of child support. He uses the baby as an excuse to try and get me back in a relationship with him. Despite the fact he lies and cheats and is unsupportive. He will gaslight situations, where I have been sent screenshotred proof and lie to me and make me feel crazy. He will often have me in tears and I had several anxiety attacks during the pregnancy. He threatens suicide and has self harmed several times when I’ve tried to leave in the past. The other day he drunk drove (he got pulled over but didn’t get fined because he blew zeros after 15mins of waiting) but he blamed me for drunk driving because he was upset about our phone call in which he yelled at me about not being able to see the baby because he had been partying in the city that weekend (and we’ve had 300+ covid19 cases in our city) and he doesn’t understand her health comes first. He doesn’t contact me to see how she is. It’s all “I miss you” and about our relationship. I feel like he uses the baby as a chip to bargain with me and to try and use against me to get back with him and get his way as he has manipulative tendencies. He also uses drugs daily, but has said he is stopping to try and prove to me he’s a “changed man”. His only interest main has been in what welfare payments he is entitled to even though he’s not a carer or provider for her.

I’m sure I’m missing things out. But I just don’t want my life or my baby’s defined by this guy! I just know he will use having his name on the birth certificate as a bargaining chip, not allowing me to move areas or take her on holidays or send her to a good private school as he wouldn’t want to pay the fees. I don’t think he has the best intentions for her or is mature enough to see what’s best for her, as all his actions right now have spoken volumes about him putting his needs first. I also don’t want him to take her one day, when he’s in a bad state of mine or suicidal, and not reply to me about where she is. Because he likes to play mind games and make me worried or take hours to reply or hang up after saying something worrying.

The Births, Deaths and Marriages place said I need his name on the application but need to give a letter explaining why he hasn’t signed it. But if they don’t believe what I write is enough to have him not sign it. They will contact him themselves and have him sign it, which will cause more problems as he will get angry about not being on there. He wants the rights of the father without the responsibilities.

Any advice? Has anyone had success in not having both parents on the certificate?

(I’m not denying him a relationship with the child. He can see her and bond with her if he chooses that’s what he wants to do. I just don’t want to be manipulated by someone who clearly doesn’t have the best intentions for this child as he’d use it as a means of controlling)