I'm in a situation where my husband and I are not together he is with other women but we both still live at his parents house... he is literally doing everything he can to make my life miserable... the only place I can go is out of state... is there a way that I can just pick up and leave since the is no legal papers of divorce or custody?

Yes, since there are no custody/visitation court orders. You can leave with the child as you have equal rights. But until you can establish residency in another state and file for divorce, he can file first and force you to return the child.

You are better off consulting an attorney and filing for divorce in Louisiana, and trying to get permission to leave the state from the court.