Father on birth certificate or not

Hi ladies,

So I'm over half way in my pregnancy now and haven't heard from the father in a few months. He disappeared with no warning when I was 3 months pregnant (we whernt in a relationship just casually dated) he said he wanted to be involved, stayed for 3 months then nothing..

I kept him Upto date in what's going on. Sent him the 20 week scan app details weeks in advance with a no show, informed him when my hospital visit is.. And yet he was a no show and no response.. I recently asked him in text for his/family medical history for the hospital and no response as per usual (I added what I needed for the hospital for family medical history in a list I was given by my doctor)

My question is.. Do I put him on birth certificate?

Can I get in trouble with the law for saying father unknown with texts to him about our baby? Especially if I receive funded help from the government

I'm in Australia btw and he lives in Australia but from new Zealand..

I just don't see the point in putting him on any documents if he refuses to even acknowledge babies existence and refuses to respond to something as important as medical history that could affect the baby..

I don't want anything from him if he can't love the baby the way she deserves.. I just don't know if this is fraud and the consequences of doing so

Thank you for the responses ♥