When i run it, it doesn't display anything, although I have test to print something inside keyPressed() method it did displayed in the console, is method drawImage() can't be applied outside the paint() method?
Yes, generally, in Java, the reference to the screen's Graphics object (called "g" in this case) is not reliable outside of the paint() method.
Standard procedure is to do all of your drawing in the paint() method, or in methods that are called only by paint(). That drawing code should look at the state of your application to know what to draw.
For example, you could have your key press set a boolean variable. Then, when paint() did its thing, it would look at the variable to know whether or not to draw the image.
And you don't normally call paint() directly. As Svend said, you would usually call repaint().