If you fear for your safety and that of your child, you can file for and very likely receive a protective order. The order may give you temporary possession of the apartment and will specify whether or not the child's father is able to have visitation with the child.
Although the child is very young and does not understand what is occurring, she may sense the danger and tension. It isn't a good environment for children, and staying in an abusive relationship can be considered failure to protect your child. If your child is present during an assault and the police are called, your abuser can be charged with misdemeanor cruelty to children in addition to battery charges and DFACs may get involved.
Contact the Georgia Domestic Violence Hotline 800-334-2836 and ask for your closest domestic violence outreach office. A domestic violence advocate can help you file for an ex-parte protective order (for free), or just help you develop a safety plan if you decide you want to flee.
You don't deserve physical abuse.
Stay safe and good luck.