It sounds like your daughter has a very early case of separation/stranger anxiety. Usually this does not occur until around six month. While some children never experience this type of anxiety, it is a normal developmental phase for most. This type of anxiety occurs because a child forms an attachment to a caregiver, typically mom and/or dad, and at the same time she develops the ability the remember objects and people who are out of sight. She starts to understand that mom and dad are permanent objects and will cry or fuss when she can’t see you or has been passed to someone else, even someone familiar like a grandparent. When you are gone from her sight, she thinks you had disappeared for good. Separation anxiety usually peaks around 18 months but can last as late as three years of age.
There are some things you can do to help her learn that you always come back and to reduce some of her anxieties.