It is not uncommon for young children, especially toddlers, to have a persistent cough when they have a virus such as a cold. Coughing can sometimes be the main symptom and may last longer than other symptoms like a runny or stuffy nose. It's important to provide comfort measures like nasal hygiene, encourage plenty of fluids, and monitor the cough for improvement. If the cough persists for more than 7 days without getting better, it may be necessary to consult a healthcare provider for further evaluation.