Father-NEED HELP- going to court for joint custody and to become domiciliary par...

[Single Father]

This is my situation I hope someone could give me some good advice.
I have a 1year-old daughter. I was never married to her mother and neither the mother or I are married to anyone and we do not live together. I have been involved in my daughter's life since before her birth. I tried to work out a verbal agreement with the mother where we would spent 50/50 time with our daughter, but whenver she(mother) would get upset she wouldn't allow me to see my baby or bring her to my home for my family to see. This has been going on for about the whole year of my baby's life. Now I'm going to court to be granted joint custody and I want to be the domiciliary parent. The mother has been sloppy with the care of the baby. She would not take the child to the doctor hence the baby missing plenty of her shots. Whenever I would try to take the baby to the doctor myself the mother would fight and not allow me. In one of those fights she hit me and I have pictures to back up my story. I had to file a police report for simple battery after she tried to accuse me of assaulting her. She is lieing and has no evidence of me assaulting her, but this matter is still being processed by the courts so I don't even have a court date for this.
We reside in Louisiana and for Katrina the mother evacuated to South Carolina. Now without consulting me the mother wants to live in South Carolina not come back to Louisiana and keep the child with her. I have the child with me now after some hard convincing and also have a temporary restriction order where the mother could not take the child from this state until after our court hearing. I am running short on time and I must be honest I am not very prepare for court. I need help on how I could be granted to be the domiciliary parent. I reside in Louisiana