I've found a document from the Children's Commissioner for England that implies that the requirement stated in my earlier comment is outdated. The comment (in case it is deleted) was:
Good question. I believe your permanent residence dates not from 2013 but 2012 (five years after you arrived). At Apply for citizenship if you were born in the UK, however, the government says that the parent must have "a permanent residence document" for the child to be a British citizen, which implies that simply being a permanent resident (without a document) may not be enough. If that is correct, then your daughter has to apply, which costs a pretty penny. – phoog Nov 30 at 19:47
The document, Briefing: the status of EU National Children in Britain (pdf), says:
The rules governing whether a child is British, or can apply for British citizenship are complex:
- If a child was born in the UK before 2000, to EU nationals who can show they were studying or working in Britain when the child was born, the child is a British citizen
- If a child was born in the UK between 2000 and 2006, to EU parents with a permanent residency card, then the child is British
- If a child was born in the UK after 2006, to parents who can show they had lived and worked in Britain for at least 5 years prior to the birth, then the child is British
- Children who were born in the UK but whose parents don’t meet the conditions above don’t have any status in British law and are only eligible to apply for British citizenship in certain circumstances.
- Children who were born in the EU but have grown up in Britain may be able to be included in their parents’ application for British citizenship, but cannot normally apply in their own right.
This says that the requirement that the parent "have a permanent residence document" applies only to those born between 2000 and 2006. For children born after 2006, as was your daughter, the requirement is to show that the parents had "lived and worked in Britain for at least 5 years prior to the birth." I suspect that this is a clumsy way of indicating that at least one parent must be a permanent resident in the UK (not that both must actually have been living and working in Britain), thus meaning that the possession of a document certifying the permanent residence is not a prerequisite to the child's acquisition of citizenship at birth.
This interpretation is reflected in a Guardian article from March 2018, EU parents warned children need papers to stay in UK after Brexit, which says
Nando Sigona, a senior lecturer in migration and forced displacement at Birmingham University, points out that parents will have to prove they were in the country legally for five years at the time of the child’s birth.
If not, he advises that parents should apply to register their children as British citizens but this will cost more than £1,000 for each child, a considerable financial barrier.
The statement that those who cannot prove legal residence for five years will have to register their children implies that the children of those who can prove it are citizens from birth.
Additional confirmation may be found from a research brief by Colin Yeo, taken from the Eurochildren blog, linked in the Guardian article. The brief (pdf) says
2.2 Parent possesses permanent residence but not documented
If the parents did not obtain a permanent residence document but had automatically acquired permanent residence nonetheless, the child will have been born British. However, to make a successful passport application to obtain proof of his or her citizenship status, the child will need somehow to locate, perhaps many years later in adulthood, evidence that the parent in question pursued a qualifying activity for a period of five continuous years.
I would expect that you should be able to apply for a UK passport for her now, submitting proof that you had a right of permanent residence at the time of her birth. However, I would not be surprised if the bureaucracy requires you to get a permanent residence certificate before applying for her passport.