From the look of https://www.gov.uk/apply-citizenship-british-parent/born-on-or-after-1-july-2006 and what you have said I think it is likely your daughter is a British citizen and just needs to apply for a passport or an immigration status letter.
sounds about right, yep! i remember i had to get a certified ‘long’ copy of my birth certificate (to prove that both my parents were British by birth) in order to register my daughter.
@hvsds started
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From the look of https://www.gov.uk/apply-citizenship-british-parent/born-on-or-after-1-july-2006 and what you have said I think it is likely your daughter is a British citizen and just needs to apply for a passport or an immigration status letter.