Consider an irregular shape in your dressing room.

Placed at an angle

I would do two really LARGE square/rectangles.....and I would consider orientals with subtle, muted colors...maybe even an overdyed. That way, the furniture is what the eye focuses on. The rug under the bed should be big enough so that when you get out of bed, your feet are on rug, not floor.

There are so many things wrong with that space, that honestly rugs are the least of it. But no, I would not put a round rug that close to a rectangular rug.