If you don't want another monitor in the cab of your truck then why don't you just use the Edge monitor? I thought that Edge made a camera for that exact purpose.
Maybe I'm off here but I just searched Google and came up with this:
http://www.edgeproducts.com/product.php?pk=129&pvk=438Edit: Seems that you're after a wireless solution because you want it on the back of the trailer and I would agree that would seem the easiest. You might try going the GoPro route. They offer a cam that can be accessed via WIFI from what I've been told. You can then access it via a smartphone or iPad.
If you decide to go the wired route then I don't really think it would be that hard to install at least from the back of the trailer to the tongue. You will need to create or buy a plug so you can easily plug the camera in when your trailer is hooked up. The hardest part of the install would be from the monitor to the rear of the pickup.
Best of luck however you go about it!