Powering a 12V and a 9V device from single power supply with LM7809 voltage regulator
The LED does not affect the load of the voltage regulator. It affects the supply. The voltage regulator's load is the 9V device.  The only way it will cause a problem for the regulator is if its current draw triggers a voltage drop below the point that the regulator is able to maintain 9V.

The main question about your circuit is: is the incoming 12 volts regulated? Or is it just the nominal voltage on a transformer device such as a wall adapter? If 12V is the maximum rating of the LED device, but the supply is unregulated, you may want an additional 7812 regulator there.

(What kind of LED is it; and does it have a built-in resistance for current limiting?)