"It is my turn" is the most natural phrasing. It is hard to rewrite it with a real subject. The best I can do is: "My turn comes next." Logically, you should be able to say "My turn comes now," but to me that sounds unnatural.

Yes, "it" is a dummy subject. The sentence is natural as written, although it is possible (if less "natural") to reword it with "the turn" as the subject. You can try that as an exercise, or ask me to do it for you if you can't figure it out.