I used a wireless baby monitor in one of my old trainers trailers
You can buy a "real" camera (take a look on the website Kramer). Horse Vision has great products, they also offer cameras with night vision. Sometimes people use baby phones and actually it works great!
I have a horse that has real difficulties to travel in a horsebox, so I installed a camera to see how he reacts while traveling. He moves a lot, scratches the ground... I bought an ordinary camera and fixed it in a corner. And then I asked a professional to installed a screen near the wheel so I can easily check what is going on while I drive. But I think if you are a little bit used to technologies, you can do everything by yourself!
It is a very good idea! You will be able to measure the impact of your driving on your horse! I do not know any special camera but I guess you can put a Go Pro, you can connect it to your smartphone. The only problem is the length of the travel...