Git, semantic versioning and how it fits into (my) a typical development timeline?

I'm working on a Q&A system and about to tag my current application with "1.0.0" for it's first official version/tag. It's about to be rolled out for beta testing to a limited test audience next. Is "1.0.0" correct at this stage?

Also, no doubt there will be many bugs found at that stage. Do I keep it as "1.0.0" but forcefully moving the tag until it's release. Or upon fixing the bugs, would I give it a new tag "1.0.1". Then after another round of testing perhaps "1.0.2"

So when working on enhancements (e.g. new features such as a new menu, new search input field) would these be minor changes as in from "1.0.0" to "1.1.0"?