C++ Factory Design Pattern

I am trying to create a factory design pattern. Am I moving towards the correct direction? Object creation is not in a separate class that manages new objects when the type is passed in as a parameter.

class PetFactory
{
public: Pet* createPet(std::string type)
{
    Pet * pet = null;

    if (type == "Dog")
    {
        pet = new Dog();
    }
    else if (type == "Cat")
    {
        pet = new Cat();
    }
    else if (type == "Rabbit")
    {
        pet = new Rabbit();
    }
    else if (type == "Hamster")
    {
        pet = new Hamster();
    }
    return pet;
}

};