Simply changing

public int compare(Dog d, Dog d1) {
  return d.age - d1.age;
}

to

public int compare(Dog d, Dog d1) {
  return d1.age - d.age;
}

should sort them in the reverse order of age if that is what you are looking for.

Update:

@Arian is right in his comments, one of the accepted ways of declaring a comparator for a dog would be where you declare it as a public static final field in the class itself.

class Dog implements Comparable<Dog> {
    private String name;
    private int age;

    public static final Comparator<Dog> DESCENDING_COMPARATOR = new Comparator<Dog>() {
        // Overriding the compare method to sort the age
        public int compare(Dog d, Dog d1) {
            return d.age - d1.age;
        }
    };

    Dog(String n, int a) {
        name = n;
        age = a;
    }

    public String getDogName() {
        return name;
    }

    public int getDogAge() {
        return age;
    }

    // Overriding the compareTo method
    public int compareTo(Dog d) {
        return (this.name).compareTo(d.name);
    }

}

You could then use it any where in your code where you would like to compare dogs as follows:

// Sorts the array list using comparator
Collections.sort(list, Dog.DESCENDING_COMPARATOR);

Another important thing to remember when implementing Comparable is that it is important that compareTo performs consistently with equals. Although it is not required, failing to do so could result in strange behaviour on some collections such as some implementations of Sets. See this post for more information on sound principles of implementing compareTo.

Update 2: Chris is right, this code is susceptible to overflows for large negative values of age. The correct way to implement this in Java 7 and up would be Integer.compare(d.age, d1.age) instead of d.age - d1.age.

Update 3: With Java 8, your Comparator could be written a lot more succinctly as:

public static final Comparator<Dog> DESCENDING_COMPARATOR = 
    Comparator.comparing(Dog::getDogAge).reversed();

The syntax for Collections.sort stays the same, but compare can be written as

public int compare(Dog d, Dog d1) {
    return DESCENDING_COMPARATOR.compare(d, d1);
}