So maybe it's a bad idea (no reference to my user name, honest...) but I personally don't think it makes any sense to get a permit for this kind of thing, regardless of whether it's required or not. You're running a ground wire 2' - simple. As long as you (or your dad / friend / whoever) knows what they're doing, it's probably one of the easiest things to do. Now, if you have no clue what you're doing and you don't trust that your dad / friend / whoever does either, then pay the electrician to put it in - touch the wrong places in the breaker box and you can quickly find that you would MUCH rather pay $150 than ever experience that.
As for your land-lord, you have to weigh that yourself. Could you install the line and new plug and then swap it back to the 3-prong before moveout? If you do discuss this with your landlord, are they going to make you get a permit and electrician? I don't know your relationship with your landlord, but in my situation (also renting), I added a new breaker and plug to the panel in such a way that when it's time to move out I can remove anything I put in and return the panel to the same condition as when I got there. As far as anyone will know, it never happened, and that's fine by me.
If the house burns down because I screwed something up... well... fingers crossed on that one (and I trust my ability to wire a breaker).
-Kevin