Willz: The big thing to understand here is that "dedication" (baptisim) in most religions is nothing like baptism for JWs. For JWs, you can only be baptized when you are old enough to choose to do so; there is no child baptism for JWs.
That's the theory; most of us know there is also the practice that any child who has the twinkle in his eye enough to say "yeth, I wanna be baptithed" will be baptized.
But for other religions it is a mystical or spiritual process that is done FOR the child. In some religions it imparts a protection to them, for others it ensures their obedience to the faith...it's not something an individual chooses for themselves. The Society quite clearly states that this kind of baptism is irrelevent in their views, no harm is attached to the child who gets baptized. When they come of age and can make a decision to dedicate themselves to Jehovah, then they can be "really" baptized.
However, if YOU are baptized, you cannot allow your daughter to be baptized. You would be associating with false religion to allow your daughter to be inducted into Chistendom, the great harlot. I take it you are not yet baptized, though, so you can be forgiven if you give in to your unbelieving mate, though things will change once you are baptized. You will be expected to take a firm stand in your daughter's upbringing, despite any resistance from your mate.
I would let her be dedicated. Nothing can yet be done to you.