Is it normal for babies to snore while sleeping? Does it mean she is excessively sleepy?

Yes, is pretty normal and occurs in about 15-25% of infants and it used to be viewed as harmless. But recent research suggests otherwise. Some babies who habitually snore were diagnosed with obstructive sleep apnea syndrome, in which the upper airways repeatedly collapse or partially collapse. This forces the baby to wake up. Other symptoms of obstructive sleep apnea include labored, irregular breathing and restlessness during sleep. http://www.parentingscience.com/baby-sleep-problems.html#sthash.Y98OcPUv.dpuf