Kids can bounce back really fast but I would see if you can get in to see the doctor in case it's some sort of infection because antibiotics in the US aren't cheap. I had what I thought was a cold flying out in 2001, within 24 hours of arriving, I was really sick. It was severe sinusitis and 5 antibiotic pills (they were strong horse pills!) cost $150. Worth getting in just to be safe.
As for the flight, unless someone is obviously ill for example throwing up etc. You shouldn't have a problem. The real issue is how will your child feel/cope more than will the airline stop her. I can't think of anything worse than having a stomach bug and being stuck on a plane!
Probably a 24/48 hour thing and she'll be fine but I think it's a judgement call you'll have to make on departure day, especially if you have other kids that may cop it get sick en-route.