Maturity is great but not for jQuery 1.2.6

Drupal 6 has jQuery 1.2.6 somewhat hardwired. The jQuery update module can get you to 1.3.2, still a long way from the current version. Drupal 7 has hook_js_alter, which will allow you to conditionally override the built-in version.

If you're looking to do some UX magic and want the latest greatest version, you can do the following:

1. Save the jQuery version that you want into a location like /sites/all/libraries
2. In your template, where jQuery is loaded, load your version before it.
3. Load a js file between the load of the two JQuery libraries, which contains this:

newJQ=jQuery;

To use the newer version, use newJQ instead of $, such as newJQ('a') or newJQ(this)