Moving out

So I'm 21 and have a 1 year old son. We live back with my mom. I use to live with his father but we separated. So I'm a single mother. But I wanna get my own place with my son. 2 bed 1 bath. I work full-time and recieve child support. So financially I think I will be okay. But I never lived by myself or really been on my own specially with a baby. As soon as I graduated highschool we moved in together. But my mother wants me to stay close. I will like to move in the next town over which is only 30-40 mins away from her. I understand she loves her Grandchild this is last one in the family out of 11 lol. But I wanna learn and do things on my own. So I wanna save and move out Feb 2019. Any tips? Or suggestions? Like I said I have never been on my own so I'm nervous.