Termination of parental rights ends all of the father's rights, as well as all of his responsibilities to the child, including the duty to pay child support. For this reason, the courts will not normally terminate parental rights unless an adoption is contemplated.
To establish paternity, and seek child support you can file for support at the Domestic Relations Office at the Courthouse. They will give notice to him, and have a conference at which time he will either acknowledge paternity, or deny it. If he denies paternity, they will order blood tests, which in almost all cases can establish who the father is.
This is not intended to provide legal advice about your situation - just a few casual remarks about a legal question. We are a debt relief agency helping people file for bankruptcy.
I agree with the previous attorney's response as far as it being unlikely that the court will terminate his rights. You can however seek sole legal custody. That will allow you to make all decisions relating to your daughter without him having any say. You may also want to confirm your sole physical custody in a court order. Without a custody order in place both natural parents have equal rights to the child and so he would be able to take your daughter if he chose to. I understand he hasn't been involved so far but often the circumstances change once support enters the equation and it's better to be safe than sorry.