The correct one would be "She feels she is entitled to have happiness." Have is used with some pronouns and plural nouns: "I have lots of apples." "You have pretty hair" "We have water for the thirsty, food for the hungry." "Girls (they) usually have long hair" Has is used with the third person singular. For example: "She has two hairbrushes." "He has a new car." "The car has a dent in it." "It has a dent in it."