Oh, tons of ways to do that, easy! I'd get Nattress or CHV plugins to do it. There are film effect plugins that simulate old worn our film. Use one, turn everything off, except the shaking variable. Lots of ways to do that.
If you want to track the shaking exactly, you can, I believe. But you'd need to use Motion or Shake. You simply place a tracking on something in the frame, attach it to a matte that covers the whole frame, copy and paste it to a new clip. It'd take some experimenting, but it could be done.
If you're trying to make something shake along with a clip that is superimposed over that clip, the same tracking methods apply. To detailed to go into in a forum post, but it's possible, once you learn one of those two apps.