My grandchild is a year old, the father is not listed on the birth certificate and my daughter is leaving him. He has said that if my daughter tries to leave with the child he won't let her. My question is can he keep the child from my daughter, since he is not on the birth certificate, and he has not done any paternity testing.

Then tell her to not make the child a pawn of the adult games and go to court right away for custody and child support issues.

No he can not stop her from leaving,
He can file for custody, prove paternity and ask court to give him 1. custody, 2, partial or joint custody, 3 visitation.

Just not being on the birth certificate does not take away his rights, he just has to prove paternity in the courts to have those rights.

So she needs to just file for custody, leave and file for child support like any other couple with a child does.

He will make normally many threats, keep the child, not let her see the child.

These are juv and does nothing to help and uses the child as a weapon. It is also not true but many women don't seem to think when it comes to this.
Also if she leaves she needs to leave, too many keep going back and back and back after they hear threats