Your poor dd. My ds was the same. Had a dreadful cough, just at night, from between about 8 months to about a year, and then it miraculously disappeared.
I took him to the doc a couple of times, as I was concerned, but every time his chest was clear, and he was always in good health otherwise (eating well, no temp etc). The GP said that sometimes in children under 2 the airways in their lungs are just really tiny, and they do get congested if they've had a cold, and it can take a while to clear. Apparently it's v common. He also went through the symptons for a chest infection so that I could easily tell the difference (shallow breathing, air sucking in from under the ribs, flaring nostrils, temperature etc). He said that if ds still had the cough when 18 months to 2 years, then they would investigate further as it could be asthma (we had no family history of this that would set alarm bells ringing earlier).
We did all the normal things we could for coughs - raised head of cot, wet towels on the radiator, vaporiser in the room, chest rubs, cutting down on dairy as much as we could etc etc and eventually it just went.
I'd take your dd to the GP to get her checked over, just incase, and ask their advice. HTH