Well, not really from Krypton.  From a small piece of it, as you'll see.

The idea of a Super-Girl was tried out in Superman #123, August 1958.  Jimmy Olsen used a magic talisman to wish her into existence; but when her life was threatened by Kryptonite, he wished her back to whatever limbo she came from.

Reader response was overwhelming, and within a year, it led to a decision.  Twenty one years after Superman's debut, another super-being of his family would become a part of DC's family.  And so Supergirl was born.

The writer was Otto Binder, a successful Science Fiction author as Eando Binder, a writer for many comics companies, but best known for his work on Captain Marvel - and Superman.  The artist was once more Al Plastino.

Supergirl kept her presence on Earth secret for the length of her stay at the orphanage.  Finally, she was adopted and became Linda Danvers.  By this time, Jerry Siegel himself was handling the scripts.  Eventually, after being revealed to the world, she discovered her parents were alive in another dimension, and freed them.

Supergirl has gone through many changes since.  By 1981, in a different costume, she lives in New York City and, as Linda Danvers, is a soap opera star.