Java OOP instantiate self or add subclass?

So the main animal class will generate som cows, but the instantiation is made in the cow class. My question is: Is this code pattern really "ok"? Or should the cow class be renamed to "CowHandler" and instead have a subclass named cow?

CowHandler would then have a field List<Cow> cows; and Cow class only String name;

It just feels strange for the cow class to instantiate itself, for example the field with list of cows is never used from within the cow class. Here is the code as of now:

Animal class

import java.util.List;

public class Animal
{
    public static void main(String[] args)
    {
        Animal animal = new Animal();
        animal.init();
    }


    private void init()
    {
        Cow cow = new Cow();

        int count = cow.getCows().size();
        System.out.println("Cows in list before: " + count);

        List<Cow> manyCows = cow.makeSomeCows();

        for (Cow c : manyCows)
        {
            System.out.println(c.getName());
            System.out.println("Children?: " + c.getCows().size());
            System.out.println("");
        }

        count = cow.getCows().size();
        System.out.println("Cows in list after: " + count); 
    }
}

Cow class

import java.util.ArrayList;
import java.util.List;

public class Cow
{
    private String name;
    private List<Cow> cows;

    public Cow()
    {   
        cows = new ArrayList<Cow>();
    }


    public List<Cow> makeSomeCows()
    {
        for (int i=0; i<10; i++)
        {
            Cow cow = new Cow();
            cow.name = "Tiny cow " + ((char)(i + 65));
            cows.add(cow);
        }
        return cows;
    }


    public String getName()
    {
        return this.name;
    }


    public List<Cow> getCows()
    {
        return this.cows;
    }

}

Output:

Cows in list before: 0
Tiny cow A
Children?: 0

Tiny cow B
Children?: 0

Tiny cow C
Children?: 0

Tiny cow D
Children?: 0

Tiny cow E
Children?: 0

Tiny cow F
Children?: 0

Tiny cow G
Children?: 0

Tiny cow H
Children?: 0

Tiny cow I
Children?: 0

Tiny cow J
Children?: 0

Cows in list after: 10