First of, for someone learning jQuery and JavaScript, you've done a great job of avoiding the pitfalls of most new developers to JavaScript;

 1. You're not passing strings to `setTimeout`, which a lot of people do.
 2. You've got a good grasp on closures (no matter how long they took you to learn :)).
 3. You're using strict equals (`===`) rather than equals.

... so, if you want me to be really, *really* picky;

 1. I don't see much point in adding your code to the jQuery namespace. It would work just as well to be added to your own namespace. A lot of people fall into the habit of defining *everything* on `$`, and are scared of declaring your own namespace; don;t be:

        var ME = {};
    
        ME.notify = function (title, msg, duration) {
            return new notification(title, msg, duration);
        };

 2. It's a code convention to use a capital letter for constructors (e.g. functions you need to call `new` on); change `function notification` to `function Notification`.

 3. You could make use of [prototypical inheritance](https://stackoverflow.com/questions/572897/how-does-javascript-prototype-work). As it stands, you're defining and adding a `hide` function on every instance of a notification you create. Obviously this has a negligible memory impact. Instead, use prototypical inheritance, and declare the function once;

        function Notification (blah, blah, blah) {
           // blah blah blah
        } 
    
        Notification.prototype.hide = function () {
            var self = this;
    
            this.element.fadeOut(1000, function () {
                self.element.remove();
            });
        }

 ... you'd then have to change your double click handler to use the anonymous function approach I recommended in [my answer](https://stackoverflow.com/a/15309663/444991), as `this` will no longer be the correct `this`.

 3. You've got a potential [XSS exploit](http://en.wikipedia.org/wiki/Cross-site_scripting). For example, given the `message`:

        <script>alert(document.cookie);</script>

 This will be injected, and evaluated in your page. You can fix this by setting the `h3` and `p` using `text()` explicitly;

        this.element = $('<div class="notification"><h3></h3><div class="notification_body"><span class="text"></span><br/><i>(double click to hide)</i></div></div>');

        this.element.find('h3').text(title);
        this.element.find('span.text').text(message);

... but again, I want to re-iterate that I'm being *very*, ***very*** picky. What you've got is well written, functioning JavaScript.