I really feel you on this, a coughing baby is so hard to watch especially when they are so little. At 6 months old it is always better to be safe, so I would bring her to the PD or polyclinic just to get her checked out properly. In the meantime, keeping the room well-ventilated and making sure she is well-hydrated can help a little, but honestly at this age I would not wait too long before seeing a doctor lah.