How to return an object of inherited class from abstract base class?

[PolishPaul]

So for practice i'm designing a class library of Animals - cow, chicken, pig, duck. I made my base class "Animal" abstract and the functions within abstract as well. Other animals simply inherit class Animal.

Here's what i'm trying to accomplish and I'm not sure how:
I want to have the base class Animal to have a function called "GiveBirth()" which simply returns a new Animal, but of the type of animal it came from. Problem is, my class is abstract so i can't return an "animal", but i have to return a specific inherited animal.

Is there a way to use polymorphism so i can just return the correct animal?

This is a member function from my base class Animal:

public virtual Animal GiveBirth() // returns, if successful, 1 or more animals of same type.
        {
            Console.WriteLine("A new {0} has been born.", (this.GetType().ToString()).Substring((this.GetType().ToString().LastIndexOf('.')) + 1));
            return new Animal(); // Won't work!
        }