If the issue section is not available in some Github repo it is because it is disabled in the Option/Features panel of that particular repo (where it has to be selected to show up)
Note though that this issue tracker is a lightweight system (which doesn't mean it is useless) that is tightly integrated with the Github repo. For instance, you can close issue from commit message. But this means it makes much more sense to use it, if the Github repo is the center of the development tools, which doesn't seem to be the case here (the 1.6 dev version doen't appear on the repo for instance). So in my opinion, this wouldn't make much sense to use this issue tracker in the present case.
Sure, I understand you can use the current Q2A site to repport bugs, but IMHO, you would have a much more efficient (and probably time saver) system if you'd have a dedicated bug tracker, and I think your application is nice enough and mature ehough to deserve one.
If you have some hosting space under hand something like MantisBT is really a nice app, and BTW it could integrates with Q2A with a SSO (I've done it for my personnal needs -though it could be further integrated as for accounts settings / view, compared to what I've done so far-).