DEPENDS. Depends on what she needs. Does she really need it? Most of the time coughs are caused by allergy, postnasal drainage. In this case she will need an allergy medicine instead of cough medicine. Cough is one of body's defense mechanism. Only give medicine for comfort. Usually Robitussin (guaifenesin) expectorants are used to help loosen up cough.Yes, she can have Robitussin (guaifenesin) if she needs it.
Yes. But i don't recommend it. Cough medicines like Robitussin (guaifenesin) (or any with dextromethorphan) have been shown over and over again, both in numerous studies and personal experience, to be mostly ineffective. You are making yourself feel better by giving it, not your daughter. You would do much better to give her a teaspoon of buckwheat honey. It's more effective and less harmful.