Just want to through my bit out there. I got pregnant at 16 and in my first year of university. I had my son 7 weeks before I began my second year and at 17.
I was, and still am, his sole caretaker. I woke up at night for feeds and changing, I buy everything for him and now I provide nursery for him.
Although I lived, and still do live, at home, I do not let anyone run around after me or him. I fit my studies around him - once he is in bed or in nursery. I stay up to all hours to get essays and studying done and I still get up when he does in the morning.
I actually made myself ill after he was born and developed bells palsy (which thankfully has gone) because of stress. Yet due to my young age doctors thought I had a serious brain condition, since bells palsy in a minor is so uncommon. Yet I still struggled through and went to university with this.
Being a parent and a student IS doable, but it is beyond hard. Late nights, early mornings, no going out and doing the student life whenever, missing class with childcare issues etc.
You just have to ask yourself whether you know you can make it work or not.