I had asthma all my life, so I can speak from personal experience and knowledge, but I am not a doctor. The specialist will be the person you need to take advice from the most (you probably knew that, I just had to put that out there).
Coughing is not a sign necessarily of asthma, coughing itself cannot cause asthma, however, coughing can bring on an asthma attack. The best thing for you to do is monitor the child's breathing, keep the child away from things that can trigger asthma just in case that is what she has. Some of the most common triggers is different animal dander, different plants (specifically those with small leaves, pedals, and parts that would become airborne easy), smoke of any kind (I can't stress this enough), and dust. What you can give her providing for medical reasons she can have it, is small amounts of honey (the more local to where you live, the better). I hope the best for you and her, but the specialist is your best bet.
Asthma can be associated with coughing.However I won't necessarily say that is the case because I am not a physician. On the other hand it could be a number of things relating to upper respiratory problems such as sinus infections, flu, common cold. I would pay close attention to the child and the symptoms that are accompanied.