Legal and physical custody of minor child

I am at the end of my rope and seriously considering leaving my husband. He doesn't help with anything related to our daughter. Okay, he washes bottles on occasion and will occasionally change a diaper and "watch" her. In any case, what does a mother have to do prove to get full physical custody of a child?  I know legal custody can be an entirely different beast. Our daughter is young (9mo).  He has never been alone with her for more than 4 hours, he has never taken her out alone, or even prepares her for her day (whether it's to go to to school or just out as a family). I take care of ALL her needs. He's never even bathed her alone. He doesn't wake up to her crying in the middle of the night, so I've do ALL the middle of the night duties, 7 days a week. We both work full time.  Any advice would be appreciated. Thank you!