Honestly, no she shouldn't be staying overnight at this stage - for the sake of good bonding with BOTH of you! She's too young. Right now, to form a secure attachment she needs to spend her nights with her primary carer, and that's you. That will give her the security to remain unstressed and as a result, she will in the longer term feel more emotionally secure and will be more confident, not less, in staying longer with her dad and not with you when she is older.
Think about it - right now, she is far too little to understand the concept of just staying over for a night, and she'll be back at home with you in a day or two. She doesn't know that. All she knows is that every now and again, and she doesn't know when or why it happens, you (her primary carer) will disappear and her bed will be different, the voices will be different, the people will all be different. She doesn't know if you're coming back - maybe one of these times you won't. This will put her under stress until you return, and it's bad for brain development and bad for her learning secure attachment - ie, that her primary carer will always be there and won't ever leave.
It doesn't have anything to do with dad and forming a bond with him - it's much more primal than that - it's about the way the brain develops. It seems counter-intuitive, but if you want her to grow up and develop strong, good attachments with her dad and his partner and his family, as separated parents, then right now make sure she sees lots of them but isn't in the situation where at any moment she might find you gone for the night - keep her home with you.