While it's a possibility, I would imagine that JA would have mentioned other symptoms, not merely coughing. I don't know what was known about the disease at the time, but a list of symptoms from WebMD includes:

* Ongoing cough that brings up thick, cloudy, and sometimes bloody mucus (sputum) from the lungs.

* Fatigue and weight loss.

* Night sweats and fever.

* Rapid heartbeat.

* Swelling in the neck (when lymph nodes in the neck are infected).

* Shortness of breath and chest pain (in rare cases).

Kitty's merely coughing is not enough to suggest TB in my opinion - if she's energetic enough to dance every dance, then she's unlikely to be suffering from fatigue and weight loss would almost certainly be noticed and harped on by her mother as [to the best of my understanding] the preferred female figure in those days was a bit more rounded than today.
The shortness of breath and chest pain would not necessarily be relevant as it only occurs in rare cases, yet that too would affect her ability to dance if she suffered those particular symptoms.
There's nothing to suggest that she's coughing anything up, which I'm sure would be noticed as illness was much more severe then that it is now - particularly TB, which was fatal at the time [to the best of my knowledge].
The lymph nodes might not have been affected, but if they were, someone would have noticed. The night sweats and rapid heartbeat would probably only have been noticed by Kitty herself [unless she shared her bed with one of her sisters], though the fever would undoubtedly result in calling at least the apothecary.