Dear Sir,

Yes she will be eligible, as for the session of 2023-24 she become 12 year old so if you complete the admission process of her in 2023-24 she will complete her 12th exam after 19 years of age that is also a good state. But it will be more better if you complete the admission process for 6th class in the session of 2022-23. And I don't think many schools are conducting the entrance exam for 6th, yes only some school are doing at the school level only where any kid can clear the test to get admission in 6th class. As she will be eligible for both  the sessions so its up to in which session you will take her admission.

Best of Luck!!!