I think the reason AJ is acting as he is in regards to Q is the real Q threatens AJ's entire "empire." AJ's entire enterprise is based on conspiracy theories. Once the Plan is over, AJ will lose all of his "theories" and he'll have nothing left to draw people in. The conspiracies he makes the most $ off of will be exposed to be facts, so there's no more hyping any of it, and the "conspiracy theories" left are going to be too ridiculous to entertain.
So, I think he sees Q as bringing about his worst nightmare–stripping him of all of his content that's worth anything. Financially, AJ HAS to try to stop Q from making all of this public because it'll spell AJ's financial ruin. (If you can find info on all of these political "conspiracy theories" in the regular news because they're now known to be true, why would you watch him?)
Just my thoughts on AJ…