The offsetParent method is only defined in jQuery 1.2.6 (from a quick code inspection of 1.2.3 and 1.2.6). So your Draggable depends on 1.2.6 I guess.
The lowercase q jquery as the first argument to your wp_enqueue_script is just a "handle" or identifier used by WordPress to track multiple requests for the same item. You seem to be using it correctly.
I have seen other plugin developers force WordPress to load their own version of the base jquery.js with the following:
wp_enqueue_script('jquery', MYURL .'js/jquery.js', FALSE, '1.2.6');
That said, I wouldn't recommend it unless you have to to avoid a bug (or missing features, such as not working with Draggable). It's also possible that by overriding it with a newer version, you might break something in someone else's plugin. Then again, the next WP release might break those plugins too :-)
(By the way, I recommend you use a fully qualified path so your plugin doesn't break if someone puts it somewhere you didn't expect (ie renames the directory, installs WordPress in a deep subdir). MYURL above is a define statement which replaces the URL to the plugin as determined by the current environment; you just need to put something defining MYURL in your main plugin code)