I have a few queries:
1. For how long does she sleep daily? (For how many hours?)
2. Don't you think that it's the job of her supervisor, and he will definitely speak to her if she doesn't perform well?
3. Why do you think that this sets a potentially disastrous precedent? (It's good to be vigilant, aware, and careful about everything at work, but a whistleblower is respected if he raises his voice in extreme situations like sexual harassment, misuse of power, etc.)
4. If everyone else is ignoring this, then why can't you focus on your performance?
5. If she trusted them and explained her problem, then why don't others and you suggest some solutions to cope with it? (Rather than creating another problem for a sick employee)
6. How is that affecting your performance and growth in the organization?
7. What steps have you taken to address her behavior and make her aware that this behavior is leading to organizational loss?
Solution
Rather than complaining about her case to seniors, you can lend a helping hand to her. Sometimes, a colleague is the one who can actually help. Maybe you are the only one who can help her.
I think it's not just about a physical deficiency only, but she might be suffering from some emotional and psychological issues as well. Moreover, there might be some problems at home or work too. If you want someone to take action against her, then it will create more problems for the employee, which I feel will definitely set a potentially disastrous precedent.
I suggest you speak to her first and try to understand the actual problem. You just have to look from another point of view as if she really needs help.
If you don't find it working, then request your HR to counsel her and if possible, provide necessary medication to the employee. The rest is HR's duty, and they can issue her a memo to explain.
(Also, if you really think that it's unethical on her part, then you can just tell her what you want to say through some stories; like, "in my previous organization, an employee was terminated when he was found asleep during office hours," etc. This will warn her indirectly and won't spoil your professional network at the office.
Moreover, there are many cases in the history of Labor Law where employees were found asleep, and some actions were taken against them, but it didn't put a blot on their resumes. You can share these cases with her to make her aware that it's not right, and she is supposed to contribute to the team.)
You can advise her to work on her biological clock, her diet, and exercise schedule, as this usually helps in cases of insomnia. Moreover, meditation and JPMR can help a person relax and sleep better. She can go for a quick tea break and climb stairs 5-6 times whenever she feels like sleeping and then come back to work.
In the end, I personally suggest you have empathy with her and try to put yourself in her shoes before taking action.
Every person is fighting a battle in life, and please don't judge anyone at first sight!!!