How to wrap oEmbed-embedded video in DIV tags inside the_content?

Question

I am making a Wordpress Theme for a website with video tutorials. I would like to put the video that is embedded in the content (with oEmbed) in a apart div.

An example

The full content (output from the_content()) is something like this:

<p><iframe src="http://player.vimeo.com/video/0000000" width="900" height="506" frameborder="0" webkitAllowFullScreen mozallowfullscreen allowFullScreen></iframe></p>
<p>This is an Test of a tutorial. Bla bla bla</p>

And I would like to get this to:

<div id="video">
<iframe src="http://player.vimeo.com/video/0000000" width="900" height="506" frameborder="0" webkitAllowFullScreen mozallowfullscreen allowFullScreen></iframe>
</div>
<div id="content">
<p>This is an Test of a tutorial. Bla bla bla</p>
</div>