Answer:
My sister's daughter (the FIRST "little girl" in the question) would be my Niece, therefore making me her Aunt.
Once my Niece had a daughter (the SECOND "little girl" in the question) she would be my Great Niece making me her Great Aunt. Now, if the Great Niece had a daughter, she would become my Great Great Niece and THEN I would be the Great Great Aunt.
You are the Great Aunt.