Many thanks for your patience. The starting point is that if she has been continuously employed at her place of work for less than 2 years then her employment rights will unfortunately be somewhat limited. Most importantly, she will not be protected against unfair dismissal. This means that her employer can dismiss her for more or less any reason, and without following a fair procedure, as long as their decision is not based on discriminatory grounds (i.e. because of gender, race, religion, age, a disability, sexual orientation, etc.) or because she was trying to assert any of her statutory rights (e.g. requesting maternity leave, etc.). In the event that the reason for dismissal fell within these categories, then the dismissal will either be automatically unfair, or there will be a potential discrimination claim.
If the dismissal had nothing to do with any of the above exceptions then she would not be able to challenge it and her only protection would be if she was not paid her contractual notice period, because unless she was dismissed for gross misconduct, she would be entitled to receive her contractual notice period.
So the only issue here is whether she could try and classify herself as being disabled. Depression can amount to a disability if it is a long term condition so really it is a matter of whether she meets the criteria and if this was the reason for her dismissal. Also it depends on whether she is prepared to take it as far as a tribunal and she may be put off by the fact that it costs over £1k to issue the claim. So you can dismiss her if needed, but subject to these potential risks.
This is your basic legal position. I have more detailed advice for you in terms of the law on disability and how it is determined whether someone is disabled or not, which I wish to discuss so please take a second to leave a positive rating for the service so far (by selecting 3, 4 or 5 stars) and I can continue with that and answer any further questions you may have. Don’t worry, there is no extra cost and leaving a rating will not close the question and we can continue this discussion. Thank you