How do I copy or clone a LinkedList-implemented Queue in Java?

you can use an iterator :

Iterator<Integer> it = q1.iterator();
while(it.hasNext())  {
   q2.add(it.next());
}

If q1 is one of JCF implementations of Queue like ArrayQueue etc are Cloneable you can use

    Queue q2 = ((Cloneable)q1).clone();

otherwise

    Queue q2 = q1.getClass().newInstance();
    for(Object e : q1) {
        q2.add(e);
    }

In a one liner:

new LinkedList<>(myQueue);

Since Queue extends Collection, and collections have a constructor that takes another Collection, this is a quick way to do a shallow clone.

Substitute LinkedList with your own Queue implementation if you wish.

Also, read the javadocs. They have all the answers.