I agree with getting the site up as soon as possible. I have slight reservations about delaying the review, only because I am worried it will be delayed too long.
Having the review makes something good happen in the Q&A: in order to do a review, someone coming here will surely get confused on one or two small points in the paper, and it is natural to ask about these points in the Q&A section. This can be answered quickly. Having a referee section snowballs the Q/A site into high-quality question mode immediately.
But one comment for Dimension 10: don't worry about anyone "stealing" ideas. It never happens. When ideas are good, nobody understands them well enough to steal them for at least a year or two.
This positive feedback between the refereeing and the Q/A is a cheap way to ensure that the Q/A is professional level right from the start. If you go public without a refereeing section, your first questions (which set the tone for the site) are going to be "Do we REALLY know there is dark matter?" "Why is 1+2+3 ... = -1/12 in string theory?" and other extremely old and well understood things, rather than "In fig 2 of http://arxiv.org/abs/1403.1254 , how sensitively does the null result depend on the background fitting?" and things like this, which one wants to encourage.
The feedback between Q/A and reviews can go two ways, as when an answer in Q/A becomes sufficiently high quality, it might merit an evaluation as a publication, in which case, you can simply copy it in the review section and ask for a vote on the same criteria. This allows the site to host original contributions locally, and this means academics need to pay attention just to avoid missing something new.
The question is the time-frame. If it is one month or two, no problem, but if it is a year, we will accumulate hundreds of student questions and then people will just feel inhibited from posting nitpicky technical questions about the guts of a paper, because the atmosphere will not feel serious enough.
But still I support going live immediately, the sooner the better. This will at least get the technical stuff sorted out quickly. I still would like to try to modify the tag system to a heirarchical thing before going live, but my laptop was stolen(!) and I can't write any code until my new one arrives.