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_deregister_script('jquery');
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 :-)
The whole javascript include system is not well documented and I'm not even sure I have figured out how to use it properly... but it appears that WordPress doesn't really pay attention to your version information. The idea seems to be to only load one copy - so if a few plugins all call wp_enqueue_script('jquery'); only one loads. It appears, though, that if there's already a jquery handle, WordPress just ignores your plugin. The deregister stuff wipes out the jquery record and then it pays attention to your path information and registers and enqueues your version.
(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)