In that CPU benchmark I linked, every chip they tested all the way down to an Athlon II X2 265 allowed 59 FPS or better. Yours would fall in somewhere between the Phenom II X2's and Phenom II X4/X6 on that chart, so with a 60 FPS goal in mind your Q6600 is definitely not the limit on your performance in Arkham Origins.
On the other hand, if you flip back a few pages to the GPU tests, in one they found the HD 6870 not even breaking 60 FPS on average at 1680x1050 (first one on this page). So naturally its going to be even lower at 1080p.
There's obviously plenty of room for improvement over the Q6600 in many other games, but I think if you're going to upgrade something the GPU is still the priority. And again, Arkham Knight is still a big unknown, aside from the fact that they're still using the same old engine. I'd probably still wait.