Once you feel comfortable playing around and adding minor effects (week or two), you might want to build bigger applications -- which is where a lot of non-jquery frameworks see their raison d'etre, by making it more obvious how to structure your applications. Some people don't even get that far, as they might do a lot on the backend level and are perfectly satisfied with jquery's innate abilities and that of some plugins provided.
So I wouldn't hurry things. If you find yourself in need of a framework for bigger apps and/or more organization with your co-workers, browse through some of the "heavier" framework at that time. Take a look at MooTools, YUI3, but also at things like knockout, backbone and JavaScriptMVC.(Maybe even SproutCore or Cappuccino)