Well whats it going to gain from knowing?
Sounds like your little girl has got a daddy who clearly loves her to bits already and WANTS to be a daddy. There are so many kids out there without, that your baby is really lucky!
Would it be for your own piece of mind? If you don't want the other potential father around then why bring it all out into the open for the chance that this other guy could get contact with YOUR daughter?
Sorry to be really blunt, but would you ever wnat your daughter to go through anything that you have?
Personally i'd do my very very best to try and forget the bastard who beat you and consentrate on your baby and the lovely guy who wants to be her daddy!
xxxxxx