How do i transition out of my department?

I am a department I hate of a company I use to enjoy. I thought it was going to be like my old department but more strict. Its anything but that. We have outlined positions we can not cross. We're not allowed to do duties of other positions but told if we work hard in current slot will move up. However it seems the people moving up slots are the ones who don't work. Than the ones who work hardest stay stuck low ranking to pick up 90 percent of the slack. Its also hard to enforce work ethics to new add ons when simply not working makes yoy move up. I am trying to transfer out into a different department thats less labour intensive and has a better chance of getting me a job When this limited term assignment is over. I just feel like I might be told no though since my current department needs the most people. Im not really strong enough for the current department and feel like I would be better at the other roles anyways. I also have 0 motivation to work this department and trying to quit as soon as possible! How do I handle this deligate situation? I also can not complain about the structure of the team set up as Im so low rank , it would be considered out of place. It would be fine if higher up was enforcing a decent work ethic and environment but this just rewards idiocy and lazyness and Im so fed up! I only been here 2 months!