Does she not need to register her before she can apply for the passport?
I think what she's trying to avoid is her daughter not being able to pass her citizenship on to any children if they're not born in the UK themselves.
Also, she mentioned registering her daughter after moving to the UK and then getting her a UK passport, but in that case wouldn't her daughter need a visa to enter the UK, as she (the daughter) wouldn't have any proof she was British? I can't see the IO letting her in on the visa waiver program, as she would actually be entering to settle with her mother.