How to trigger a transistor from iphone's audio output jack?
A transistor will need about 0.65V to start conducting, so the iPhone's output is indeed too low. The lowest part solution to get a higher voltage will be the transformer. You'll need a winding ratio of 1:10 to get a decent output level.
You have to rectify the amplified signal. If you were just to average it using a capacitor you'd get 0V. You don't need full rectification, however. You can do without the negative part of the signal; there will always be enough positive signal to work with. Feed the signal via a diode to a capacitor. This will get you a peak detector: the capacitor will load to the positive peaks in the signal. Of course when the music stops the charge should also disappear. You can discharge the capacitor via the transistor's base resistor (missing in your drawing), and if you want to discharge faster have another resistor parallel to the capacitor.