I think end of Sept., beginning of Oct. seems about right. That's when I sent mine. I was super eager to start emailing profs, too, but I figured it would be less useful at that point. I got a response from I think everyone I contacted at that point & everyone seemed to know whether or not they were taking students at that point.
I might take the extra time to sure up my list of schools. It took me a much longer time to narrow down schools than I thought. The school I will be attending in the fall actually got added to my list at the last second, due to the suggestion of one of my recommenders. It had never made it to any of my first lists & now that I am going there I can't believe I originally passed over a program that was such a good fit for me!