When Can My Child Go Out?

Typically 4 the 1st 6 months I heard that as a mom you are attached to your baby... especially when feeding. because they feed so much. and even when you pump, the milk doesn't last as long, etc. The father and I are separated and I was wondering when can I give him to his father and allow him to spend the night? Especially when I am not doing infant formula or pacifiers.