AFAIK Centrelink will only pay you the base rate of FTB if you have not lodged a claim in with child support. I think the only ways you can get around this is if the father truly is unknown, or there is a risk to your safety by having to be in contact with him - in which case you would need to speak to a social worker.
I don't know the rates offhand, but the base rate is considerably lower than what you would get if you did declare the father/claim for child support (depending on his income).