Anything can mold as long as there is moisture or a food source. However, carpet that is kept clean and dry, including carpets made of natural fibers such as wool, shouldn’t have a mold problem.
If your carpet gets wet, dry it quickly! Mold does not grow on the carpet, but rather on the dirt on the carpet. Additionally, locate and repair the source of the moisture to prevent it from coming back. It is best to call a professional water restoration cleaner in order to ensure all mold is eliminated. A quick Google search of "water restoration cleaner near me" should help you find a local professional.
If you are worried about cleaning the carpet, know that carpet that is wet cleaned should be dried within 12 hours. Carpet that is properly extraction-cleaned should not be wet long enough to mold. If you decide to rent a cleaner and do it yourself, make sure to follow the instructions to avoid issues like mold. A quick Google search of "carpet cleaners near me" should help you find a professional in your area to do the job for you.