It's not clear, from your post, whether your daughter holds a UK passport or an Indian one (or, indeed, a passport from another country).
Any foreign national entering India requires a visa. (This must be issued prior to travel. It can't be issued on arrival). A visa is only issued if the passport has 6 months validity on it:
http://www.hcilondon.net/visa/visa-requirement .html
As far as I can tell from the Indian High Commission website, as long as the passport is valid (and has a valid visa in it), it will be accepted for entry into India. So, if your daughter's passport already has a valid visa, it should be acceptable for entry into India. If you wish to check on this, use the contact information, here:
http://www.hcilondon.net/services/contact-us.h tml
If your daughter holds a UK passport (or any other EU passport) she will have no problem re-entering the UK on New Year's Eve.
If your daughter holds an Indian passport, she will have no problem leaving the UK or entering/leaving India. If she has the right of residence in the UK, she should also have no problem re-entering the country.
Chris