I have done exactly what you are wanting. Your portable DVD player must have an A/V input. I have not been able to find a cable to do exactly what you want, but have connected 2 cable together to make it work. Out of the iPod I have the A/V iPod cable connected to the A/V input cable that came with my portable DVD player. You can't simply use a standard Mini jack to mini jack cable because Apple switched the audio and video cables, so you have to have them attached in a different order. That is why I use and iPod cable, and the A/V cable that came with my DVD player. I then just hook them together with the connector you see in the pictures. Hope this helps.
I am sure they did it just to sell a proprietary cable, even though a standard cable for a video camera or anything else will work, as long as you change up the video and audio correctly. I would love to find a 1/8th mini cable with the mini jack on both ends that was converted. It would be perfect for going from the iPod to a portable DVD player and other such devices. I found this URL to make a converter cable, and you could always just put a 1/8th jack on each end. http://www.oreillynet.com/mac/blog/2006/03/create_an_ipod_video_converter.html