Please look back at my recent questions. I just went through this myself (not my child). I had a cough so bad I couldn't talk or walk long distances. I spent a lot of money on asthma medication to "see if it helped." I finally self treated with Prilosec OTC and watched my diet for a few days and ta-da, the cough started to go away. It's been a long road, I'm on a coupld perscription drugs, and it has taken months to feel 100%. I had endoscopy and all that was detected was gastritis indicative of mild acid reflux disease. The GI doc told me sometimes the acid can get so bad, that it backs up into the bronchi and honestly affects breathing. As well, the acid can cause a gag like reflex (feels like you have something stuck in your throat) and that can cause coughing too.
I don't know if tha tis what you are facing with your daughter, but it is certainly a possibility. The main thing they would probably worry about is finding the root cause, because long term reflux can cause precancerous conditions - not that she probably would worry about that until adulthood, but years and years of even mild reflux could set her up for problems as an adult.
I should add - I had very minor symptoms of reflux. I only really noticed that I had an occasional sour stomach or mild indigestion after the cough came on. I might never have thought about acid reflux without the cough drawing my attention to it.
For me, they did an endoscopy to look for precancerous changes (not knowing how long I had reflux) and also took samples to look for infection (H pylori). Additionally, they wanted to make sure I didn't have a hernia or ulcers. All these things, at least in adults, can bring on reflux symptoms. I don't know how they might treat or diagnose a child. I know an endoscopy woudl be scary - I was scared - but it was ultimately really simple and reassuring to know I was okay.
Let me know if you have any questions. I'm the of an 8 year old girl too. I imagine how hard it is not to know what the problem is. It's good GI issues were brought to your attention and in my experience is a likely cause.
PS - I avoid fatty, greasy, and carbonated foods which are my triggers for indigestion, sleep with an extra pillow to elevate my head, and take Protonics and another medication to coat my stomach (sucra-somthing or other). I am weaning off the meds to see if I do okay. I also don't eat about 4 hours before bedtime.