I have a wheelstand(click here for pictures) that is 2ftx2ft roughly and I can just move it to the corner of the room. The only change I had since the pictures is screw a rubber mat(easy to cut the mats up with a scissor) under the stand. From what I know so far is that diamond shaped rubber seems to grip the best in carpet.
You should also note that wood can warp so you can make use of the rubber mat to even the base out.