Observer Based Control System Design
Your feedback matrix K seems to be off; it yields poles at {1/3, 1/2}

For single-input observable systems, you can apply pole placement to place the observer poles wherever you like (as with the state feedback poles).

You might want to review just what a state observer is so you can better understand what you're building. The equations of an observer-based control system will include the both the system state equations and the observer state equations.