Is it normal for my baby to fall asleep sucking her thumb?

Yes: All babies need to develop self-soothing skills and many babies do this with non-nutritive sucking (for example, thumb-sucking). The fact that she has learned to soothe herself with her thumb and to fall asleep with that is both normal and wonderful. Most babies will drop thumb sucking on their own in toddlerhood, though some keep it going longer.