If you're looking to extend the reach of your animated element beyond the confines of the browser window, you may find yourself hitting a roadblock with just js/css alone. However, if the animation is contained within the browser viewport, jQuery could come to your rescue. Check out http://jquery.com
Within the jQuery library, there are abundant animation APIs at your disposal that can achieve the effect you described - from cloning an element, moving and zooming it in unison, shifting its position, scaling it down while also integrating it into a new location within the DOM tree. Moreover, tweaking the animation speed and acceleration can be effortlessly achieved with easing functions.
I've whipped up a fun demo on jsfiddle where a cute rabbit hops into a bucket - take a look here: http://jsfiddle.net/ydMAB/
In the aforementioned fiddle, the bunny's movement lacks curvature. To rectify this, consider incorporating the path plugin for jQuery, accessible via https://github.com/weepy/jquery.path
UPDATE: I've included a demo link and switched over from jquery-ui to vanilla jQuery since it adequately caters to the fundamental animations needed in this scenario. Furthermore, I've shared a resource for achieving curved animations using a path plugin.