Does my Daughter has Custody of my granddaughter?

I'd say so, yes, because there is no custody agreement in place.

if he contests it, or if she wants any child support, then she would need to go to the courts to get a sole custody and child support agreement in place.

If the father has not been established through the courts then she is the sole custodial parent until then. I strongly suggest she does establish him though, for visitation and child support. (though you can get child support without the courts)

No she does not have sole custody until there is something filed in the courts. No one has custody of a child regardless if their married or unmarried. There has to be an agreement.

I've been in this same situation. just because it doesn't say he is the father, he is recognized as the father, so he has the same rights as you do. so get your papers filed and get them filed fast!