Centrelink help

Hi,

So I have an awkward question, this applies to Australians, so me and my baby's father have been split up for a year and he has main custody of our son who is 16months old, as I work full time I see our son regularly but he stays at his dad's house, well one night we had sex after a couple of drinks and I am now pregnant again, we are not together but I don't want to get rid of the baby. How do I go about it with putting him on the birth certificate without them thinking we are in a relationship? He currently claims full single parent of our son, I don't want them to think we are being suspicious when we are not and when I have the baby I will have them both part time and cut my work shifts down to almost half.