Not your seat is it? My seat creaks a fair amount sometimes, and, like you say, it's exactly that kind of "bed spring" noise, and doesn't sound like it's coming from outside the car.
Another prime suspect would be the infamous clutch squeak, but it doesn't seem like you're changing gear in the video.
Does it happen every time you pull away? It seems to be when you're already on the move, is it at the same speed everytime?