There are many causes of cough including asthma, postnasal drip, and
gastroesophagealGastroesophageal reflux disease
Gastroesophageal reflux in infants refluxGastroesophageal reflux disease
Gastroesophageal reflux in infants
Hiatal hernia repair
Reflux nephropathy
Vesicoureteral reflux disease (GERD). GERD is the back flow of stomach contents, including digestive juices, into the esophagus or food tube and sometimes as far up as the throat and mouth. There is another type, called habit cough that is just what the name suggests, a cough that might have initially had an organic cause and then became a habit.
You might want to contact the nearest children's hospital and ask if they have, either a cough clinic, or a pediatric lung specialist with an interest in cough.
The human cough reflex is significantly diminished during sleep and this may account for her not coughing while she sleeps.