Perhaps a picture will speak a 1000 words...
The LED really needs to be connected on the collector side of the transistor, not the emitter side.
John Monks suggests 270R, I suggest 330R for the series resistance for the LED. Really the difference is insignificant, you could use either (a lot depends on the LED anyway)
I have also turned the circuit around so that it's drawn in a conventional manner which makes it easier to understand for those of us that look at these things all the time
John's other suggestion about the 22K resistor is correct. LDRs differ a lot, and you could play with this resistor (some value between 1000 and 100,000 (100k) ohms would be the expected range) to get the LED to begin turning on/off at some appropriate light level.
You could place a 100k trimpot in series with a 1k resistor which would allow you to adjust the sensitivity.
Beware that the light from the LED should not reach the LDR or the turn on/off light levels will be affected.