If the room is smaller than about 14 by 16 feet, yes. You want 18 to 24 inches of bare floor between the rug and the wall. Below that the room feels tight.
What size dining table fits a 9x12 rug?
A table seating six to eight, roughly 36 by 72 or 40 by 84 inches. That leaves the 24 inches of clearance chairs need on every side.
Does a 9x12 work with a king bed?
It is the best size for one. Placed perpendicular to the bed, it gives you 18 to 24 inches on each side and 24 or more at the foot.