Thats not an all bad idea, you could implement the infared through Girder, but it is probably more work than its worth. Unless you really need that small of a keyboard, and can't find a wireless one that small, a standard wireless keyboard would be easier to setup and probably cheaper.
True, it wouldn't take that long to setup, I guess my only concern is compatability. It obviously wont work in BIOS, but I guess it should work fine once windows has loaded. Try it out and tell us how it works.