embedded c++ : dynamic typing without dynamic allocation?

Here's my issue, simplified:

• I have a code in C/C++, C for services, C++ for handling.
• I have an interface in C that returns a structure RawData that contains information which is cyclically updated.

    enum AnimalType_t
    {
                DOG                         = 0,
                GREY_HOUND                  = 1,
                IMMORTAL_JELLYFISH          = 2,
    };
    struct RawData_t
    {
        int             age;
        AnimalType_t    typeOfAnimal;
    };

    RawData_t GetMyCurrentRawData();//returns the current raw data
    bool      IsDataReady(); //returns true if data is ready, false otherwise

• I have a virtual mother class "Animal"

    class Animal
    {
    public:
        virtual Animal();
        virtual ~Animal();
        int GetType() { return rawAttributes.typeOfAnimal; };   //the only implementation for all children
        virtual int GetAge() { return rawAttributes.age; };     //to be implemented in the child class
        virtual void UpdateAge() { rawAttributes.age++; };  //to be implemented in the child class
        virtual int GetNumberOfLegs() = 0;                      //to be implemented in the child class
    private:
        RawData_t rawAttributes;
    }

• I have a known list of animals which inherit from the mother class.

    class Dog : public Animal
    {
    public:
        Dog(RawData rawData):Animal(rawData){};
        int GetNumberOfLegs() {return 4;};                  
    };

    class GreyHound : public Dog
    {
    public:
        GreyHound(RawData rawData):Dog(rawData){};
    };

    class ImmortalJellyFish : public Animal
    {
    public:
        ImmortalJellyFish(RawData rawData):Animal(rawData){};
        int GetNumberOfLegs() {return 0;};      
        void UpdateAge() { return;} override;
    };

• I have a class "Building" in which there is one, only one, animal but I don't know its type when I instantiate the building.

    class Building
    {
    public:
        Building(){};
        //sorry for the long line, but you get the idea...
        int Display(void){if(IsDataReady()) DisplayOnScreen("This animal ( "+ animal_m.GetType()+") has " + animal_m.GetNumberOfLegs() + "legs and is " + animal_m.GetAge() + " years old\n";};
        int Live(void){currentDiagCode_m.UpdateAge();};

    private:
        auto                        animal_m; //?? not working
    };

    static Building paddock;
    static Building farm;

    void Buildings_Step(void)
    {
        paddock.Live();
        paddock.Display();
        farm.Live();
        farm.Display();
    }

Here's where i'm struggling:

• allocate memory for an animal in a Building without knowing its type during building instantiation,
• type and attributes of the animal might change cyclically In other words: is dynamic typing with static allocation possible? Then, how can I call these instances so the right method is called?

Here're my constraints:

• embedded system
• no dynamic memory allocation

I though about :

• factory design pattern with unique_ptr which works great!!!... but, on the heap :(
• Object Pool?
• dynamic typing: but non possible without dynamic allocation, is it?

Is there any design/model that could fulfill my needs?

Thank you!