I want to start running to improve my fitness but I am embarrassed.?

I don't think you would feel comfortable running along the abandoned road, there is a reason your parents drilled the 'stranger danger' stuff into you and if you twisted an ankle or something and couldn't walk you might be hard to find. Your dog might be able to keep up with you but consider they have to train to be in condition too. It might be best not to put the dog through that, especially in the summer heat. A miniature poodle can't really protect you. I suggest you run along the highway (facing the traffic) and believe me, when people see a runner, they admire that they go out and run and get exercise, not what you could possibly look like. Good luck!