Your question's answer should be (a).
Your (b) answer is not wrong either,but it would be more suitable to be used when you're referring to two or more animals
-What is/are your favorite animal/-s?
-My favorite animal is dog
-My favorite animals are cats and dogs/My favorite animals are dogs
Same goes for your second answer
-What is/are your favorite fruit/-s?
-My favorite fruit is banana
-My favorite fruits are banana and apple/My favorite fruits are apples