You can ask the court to order the abusive person to move out as part of a 209A protective order. But there are many things to think about.
The most important thing to think about is whether you are safe at home. If it is dangerous for you to stay, even with a protective order, you may want to move out. A counselor at a battered women's program may be able to help you decide.
But think about this, too: under a 209A order, the person who gets to stay in the apartment gets to keep the personal property that is in the apartment. The person who leaves must go to court if he wants to get any property left behind.
Do you and your child need things like cooking pots, favorite toys, knives and forks, beds, and a kitchen table? When you get the 209A protective order, you may want to ask the court to order the abusive person to leave your home so that you can stay in it. If you want to move somewhere else after that, at least you will have time to find a place so that you can move and keep your furniture.