Firstly, look at other basic astronomy presentations by famous and popular professional astronomers. You can get excellent ideas from their works. Select out and use the strong and interesting points they used. Also, an introductory astronomy textbook table of contents would give you an outline to follow.
I would start the presentation with where we are now: our Earth and then move outwards. Next, our satellite, the moon (and mention our man-made satellites). Next, the Solar System: the Sun, planets, and asteroids. Continuing outward, show our solar system’s position in our Galaxy, the Milky Way. Then galaxy clusters and voids.
A few minutes on the history of astronomy from the ancients: Stonehenge, Mayans, through the Arabs (nearly every star name is Arabic), to the medieval astronomers would be appropriate. Explain what a constellation is and how the ancient people saw those figures in the heavens. Be sure to show sundials, the first astronomical instruments.
Telescopes are the primary instruments of astronomers. Any introductory
Astronomy presentation should include telescopes. Good idea suggested above, about Galileo and his telescope. Include gamma-ray, x-ray, optical, infrared, and radio telescopes (show the EM spectrum). Include the very large (~10Meter) and the Hubble Space-based telescope. Explain why many are located at high and dry places. Explain the idea of “lookback time”: how we are seeing further into the past as we look at more distant objects (light travel time). If you have access to a small telescope bring it along and set it up for viewing afterwards. You do not need nighttime stars to show how a telescope works.
You did not mention the use of visual aids. Your presentation will be vastly better if you can project images of your subjects on a big screen. Your library may have slides for loan, or a University Astronomy department may have visual aid resources. Of course, you may pull images from the internet and project them from a laptop.
You mentioned your audience will be “special kids”. Do not expect them to grasp stuff like the big bang, dark matter, and dark energy. Besides, those fall under the subject of Cosmology or Astrophysics, and not Astronomy. Organize your topics to fit within your 15 minute time limit and practice your delivery beforehand.
Here are a few websites that may help with organizing your presentation:
http://astronomyonline.org/Science/Tools.asp
A look at our place in the Universe. An edited version, taken from the award winning TV series "Cosmos", by American Astronomer, Carl Sagan.
Here we look at our place in the Universe, and find that we are in no way, the center of our Universe, ...we are not even the center of our own galaxy, the Milky Way;...nor our own solar system. 5:48 duration
http://www.theastronomers.org/view/164/ancient-astronomy-best-of-carl-sagans-cosmos-17/