My son has had something similar on and off for a couple of months. We've been told it was allergies, he had a cold, reactive airway disease, etc. But the one thing that has helped the most is to do percussions on his back and sides. (We were instructed to do so by his respiratory therapist.)
You hold your hand like a cup as if you have water in it and gently but firmly pat them on the back. (Now it is going to sound like you're patting her harder than you are but that is due to the way your hand is cupped.) It helps break up whatever is in the chest and makes the cough more productive. Since your daughter is young, you will most likely have to suction out the mucous when she begins coughing it up since she can't spit it out.
You do the percussions starting on one side of the back at the bottom of the lung and work your way up, move to the next side doing the same thing, then the actual sides. You will want her laying on her stomach on your lap with her rear slightly raised (like on a pillow or with one foot flat and the other on the toes).
It usually takes me about five minutes to do the full cycle - 1min on each side and about 1min total for the readjusting/moving. When he is sick I do it when he first wakes up and before he goes to sleep. I also do it whenever I hear the rattling in his breathing whether he is sick or not.
I really hope this helps out.