No! I don't believe there is anything for which you are too old except maybe Olympic Women's Gymnastics. ;-) Many fine directors have come to it later in life, usually, but not always, after some years in a related field like acting or crew work behind the camera.
At your age, you could still choose to go to film school, but, again, many have achieved great things as directors without doing so. There are many paths. The important ingredients are vision and passion.
Try to get inside the heads of your favorite directors. Watch great (and not-so-great) movie's with questions like these in mind: How does this scene further the story? Why did the director choose to shoot this from this angle? How was this shot accomplished? Does the editing serve or distract from the storyline. What might I have done differently? What made this film (or scene) work (or not work)? You get the idea. Be very analytical.
Next, try reading stories that you have not seen as movies and picture it as a movie in your head. I don't mean just the normal visualization that we all do when reading or hearing a story, but a real, shot-by-shot vision of how YOU would make it look to make the story compelling. Think about color, lighting, camera angles, and a style. Try to hear the sounds of the story and smell the smells. Think about where you would and would not want music and what sort of music it would be.
With this sort of practice, you can begin to develop the mind of a director and your unique voice as a storyteller. Now, get a camcorder and start making short, compelling films that tell a story and convey a feeling or an idea.
Good luck!