1. Your daughter may be eligible to apply for
registration as British citizen under
section 3(1) of British Nationality Act 1981,
subject to discretion, using form
MN1.
2. Such an application cannot be made any earlier than either parents' naturalisation application (or before either parent has already naturalised).
3. Since such an application can only be made in country, your daughter will first need to apply for
entry clearance as
child of a settled person / British citizen (depending on whether you hold settled status or British citizenship at the time of such application) and then travel to UK.
4. Given your circumstances (divorce), you may to prove, at the time of entry clearance application, that you have
sole responsibility / custody of the child or provide evidence that the mother of the child has no objection for the child to live in the UK with the father (e.g. - in case of joint custody).
5. The evidence(s) explained above (point 4) may also be required at the time of registration (as British citizen) application of the child.
6. For children under 13 years of age, there is no residential requirement normally for registration as British citizen, but the future intention to remain in the UK may have to be proved.
See
Chapter 9: Registration of minors at discretion for detailed information about registration of minors at discretion.
As for your naturalisation
application (form
AN), you must state the fact(s) in the application form - so if you are legally divorced, state so and, if asked for in the form / guidance, provide evidence of the same (e.g. - decree absolute).
regards
