Any reason you are moving the living room door? I guess it is slightly more optimal to have the handle nearer the front door / bottom of stairs and maybe will give a better first impression than looking at the corner of the room, but generally doors are setup that way at least in traditional houses, to give some privacy to people in the room when entering (i.e. doors are normally pivoted on the 'big side of the room'). Current layout, you push the door ajar and see very little. Future layout, you push he door ajar and see half the room. Of course, depending on lifestyle this may be a complete non-factor nowadays.
If you are going to move the door, personally I'd move it much further, much nearer to the front door and bottom of stars, to reduce unnecessary foot traffic in the hallway (bearing in mind you'd use the double doors to access to the dining room, playroom, kitchen, utility room etc, the main reason for using that side door would be to go upstairs or exit the front door, more common than using the downstairs WC I'd imagine).