Use a JButton to add new panels at runtime

I feel as beginner I may have bitten off too much in regards to application building. That said, I am working on developing an application for a friend that will have prompts where each JPanel will provide fields to create an object to be used later. What I would like to have happen is that when the panel loads, it displays one object creation panel and a button to dynamically add a new panel if the user wants to make multiples (the plus button would add the new panel).

I have drawn up something in paint to illustrate this:

(crud, looks like I can't add images yet...) Here is a link: http://ift.tt/1BuUbP4

By my very limited understanding, I can create a panel to hold these sub-panels, and then add a action listener to the '+' button to create new panels. The only way I could think to implement this is to create a constructor for the panel I want to add. Is this possible? Let me show you what I have:

package com.company;

import java.awt.*;
import javax.swing.*;

/**
 * Created by Travis on 3/1/2015.
 */
public class MainSnakeGui extends JFrame{

    protected int panelCount;


    //row 1
    JPanel row1 = new JPanel();
    JLabel splitSnakeLabel = new JLabel("Create a Split Snake", JLabel.CENTER);

    //row 2
    JPanel row2 = new JPanel();
    JButton addButton = new JButton("+");



    public MainSnakeGui() {
        super("Snake Channels");

        setSize(550, 400);
        setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        GridLayout layout = new GridLayout(5, 1, 10, 10);
        setLayout(layout);

        FlowLayout layout1 = new FlowLayout(FlowLayout.CENTER, 10, 10);
        row1.setLayout(layout1);
        row1.add(splitSnakeLabel);
        add(row1);

        GridLayout layout2 = new GridLayout(1, 2, 10, 10);
        row2.setLayout(layout2);
        row2.add(addButton);
        MainSnakeConstructor snakePanel = new MainSnakeConstructor();
        row2.add(snakePanel);
        add(row2);

        setVisible(true);
    }

    public static void setLookAndFeel () {
        try {
            UIManager.setLookAndFeel("com.sun.java.swing.plaf.nimbus.NimbusLookAndFeel");
        } catch (Exception e) {
        }
    }

    public static void main(String[] arg) {
        MainSnakeGui.setLookAndFeel();
        MainSnakeGui frame = new MainSnakeGui();
    }
}

Here is the constructor:

package com.company;

import javax.swing.*;
import java.awt.*;

/**
 * Created by Travis on 3/1/2015.
 */
public class MainSnakeConstructor extends JFrame {

    public  MainSnakeConstructor () {
        JPanel splitSnakeRow = new JPanel();
        JLabel snakeNameLabel = new JLabel("Snake Name");
        JLabel channelCountLabel = new JLabel("Channel Count");
        JCheckBox artistSuppliedCheckBox = new JCheckBox("Artist Supplied?");
        JTextField snakeNameTextField = new JTextField(30);
        JTextField channelCountTextField =  new JTextField(3);

        GridLayout layout = new GridLayout(3,2,10,10);
        splitSnakeRow.setLayout(layout);
        splitSnakeRow.add(snakeNameLabel);
        splitSnakeRow.add(channelCountLabel);
        splitSnakeRow.add(artistSuppliedCheckBox);
        splitSnakeRow.add(snakeNameTextField);
        splitSnakeRow.add(channelCountTextField);
        add(splitSnakeRow);
    }
}

Please excuse my ignorance in advance. If you have any resources for me, or if you think this might be a poor implementation of what I am trying to accomplish, please don't hesitate to let me know. Thanks in advance.