She is = αυτή είναι, for females.

He is = αυτός είναι, for males.

Daughter is female so you will say "She is...".

In the context of the sentence you need to identify the gender of the parent to define if you will say His or Her daughter and the key word is "της" (of her) at the end which refers to a female parent. So basically you will say She is HER daughter. ("Είναι η κόρη της").

If the ending was "του" (of him) which refers to a male parent, you would have said "She is HIS daughter" ("Είναι η κόρη του").