I get the feeling you are trying to find a solution to a what you interpret as a problem and probably is just fine.

My guess is that your interpretation is further influenced by the fact your daughter was born prematurely and your first kid did not do what the second does.

What you describe is a very healthy little girl developing just like one would expect it! I suggest you concentrate on this. She's "completely healthy", "has solid, completely uninterrupted naps", "does a lot of baby talk", "runs for hugs" aso. Like any kid that age, she "tosses and turns" in sleep.

The only thing I see is that she "falls out of the bed and sleeps on the floor". Just like anyone else, that should not stay so. It's ok to try to have her sleep without side bars but if she keeps falling, step back. She might not be ready yet.

My daughter is a few months older and really disliked sleeping without bars so we installed them back. She had episodes of night whining too that naturally disappeared after a while. She also had a very long episode (4-5 weeks) of sleep coughing. That did not wake her up, though, just like yours, and that did not visibly tire her either, so why worry?

Like we did in this case, go to the doctor if you wish to make sure it really isn't anything serious. And if it really isn't, then let your daughter be and it will go eventually. Kids have such phases that come and go.

Sometimes there is only a problem in the fact we think there is a problem. Focus on the positive, less on the negative.

Wish you and your family all the best!

What you interpret as a problem might be just fine.

Even if you consider what you describe to be "a problem", refrain from relating it to premature birth. Prematurely born kids are known to be more likely to develop problems than other kids but not every problem they have is necessarily due to it.

You describe a very healthy little girl developing just like one would expect it! . She's "completely healthy", "has solid, completely uninterrupted naps", "does a lot of baby talk", "runs for hugs" aso. Like any kid that age, she "tosses and turns" in sleep. I suggest you concentrate on this and much less on the fact she was born prematurely.

My daughter is a few months older than yours and had episodes of night whining too that naturally disappeared after a while. She also had a very long episode (4-5 weeks) of sleep coughing. That did not wake her up, just like yours, and that did not visibly tire her either, so why worry?

Like we sometimes did with our daughter, seek professional advice if you wish to make sure it really isn't anything serious. And if it really isn't, then let your daughter be and it will go eventually. Kids have such phases that come and go.

Sometimes there is only a problem in the fact we think there is a problem. 
Try focusing more on the positive, less on the negative.

On a side note, I think she shouldn't "fall out of the bed and sleep on the floor". It's ok to try to have her sleep without side bars but if she keeps falling, step back for a while. She might not be ready yet.