If your daughter has been coughing only at night for a few weeks and does not have any other symptoms like fever or nasal discharge, it is possible that the increased salivation from teething could be causing her to cough. It is important to continue monitoring her condition and seek medical advice if her symptoms worsen or if new symptoms develop. Cleaning her nostrils with saline water before bedtime may also help. Remember that cough syrups are not recommended for children under 6 years old. If you are unable to identify the cause of her cough or if it persists, it is best to consult with a healthcare professional.