Because definite articles in Romanian are gender-specific. We use "o" for feminine nouns and "un" for masculine ones, therefore "o fată" was the only correct option.
Fetiță would be "little girl". The ending "ță" in this case is a diminutive suffix added to "fată" to make it "smaller". I hope that helps.
When the noun is in singular, "o" is for feminine noun genders and "un" is for masculine and neutral noun genders. O fată - două fete; Un băiat - doi băieți; Un lucru - două lucruri (A girl - two girls; A boy - two boys; A thing - two things)