Yes, a lot people go jogging with their dogs, and no it's not weird to go jogging at the age of 15. It's healthy and you'll get in good shape. There's absolutely nothing wrong with being a 15 year old going for a jog.
That "prophecy" was written during the Cold War, when there was much larger tension between the United States and Russia. At the time a World War between Russia and the United States sounded much more likely than it does now. No, I don't think Russia is planning on attacking with any secret...