Sleep?!?

I usually sleep fine unless I have to get up to go to the bathroom. But I have been waking up at 6 to babysit my cousin and I'm so tired I can barley keep my eyes open so whenever she takes a nap I do too but it doesn't really help I'm still so tired. I'm pregnant and I'm afraid that when the baby comes I'm not going to be able to stay up. What if I fall asleep on the baby? I'm so scared.