Somewhat read dependant. With TT-JJ and AK, I think villain would be inclined to either push preflop or just call, not reraise another 4400, which is dying for a call. I think you can fold this. If you think villain will do this w/ TT-JJ, AK, or a lesser hand, by all means, push. Still, I hate folding QQ preflop too, but if I had a clear head, I would.