The first few days of breastfeeding can be quite difficult and you need to make sure you have experienced support to help you through the tough spots. You need to be able to arrange your schedule so you can get adequate rest, eat and drink appropriately and set aside private time for pumping. Even if you end up nursing and supplementing with formula, any nursing is better than no nursing at all. She says she's scared and doesn't want us to fall asleep before she does. This may just be a normal phase.
Children do go through cycles of significant fears.
It is important to validate your daughter's fears and don't discount them. Discuss this with her and work out a plan that will help her without hurting you. There are two important questions that you need to ask in your situation. With this she may need help or guidance from a counselor. She should not be allowed to let her fears or concerns run your household.