Elle est ma fille/ma copine is also correct!
"c'est ma copine" or "c'est ma petite-amie" (not 'Elle est' and not 'ma fille' = daughter)
Why not 'elle est'? When would you use 'elle est'?
As I know .. You can say elle est + adjective like 'elle est rouge' however with nouns you should use C'est
I think "ma fille" should be considered correct, though. In English, "my girl" can mean "my daughter". This sentence isn't precise enough to exclude either meaning.