This is a hand written copy of her original birth certificate written in 2011, because of when the copy was made the annotation is in the same hand, so it doesn't indicate adoption from birth.
I have similar copies for two children which are both annotated adopted, although they were several years old when they were adopted.
There would be a second certificate issued in her new name when she was adopted, there would be no indication of the adoption on the new certificate.
Fairmile House was the workhouse which later became Christchurch Hospital, it was recently demolished and the site redeveloped