With Q&A sites, you should naturally start ranking for question keywords. These tend to be fairly easy to rank for from my experience. I used to own a Q&A autoblog that got indexed and ranked so easy until Yahoo Answers killed their API.
Just keep your site regularly pumping out the Q&A, and your site should start generating good traffic in no time. Also promote/share your Q&A site on other QA sites like Quora, Yahoo Answers, Answers, Blurtit and others as well as social media like Facebook, twitter, reddit and more in order to broaden your reach.