Best to submit by October, if you can. I know I didn't have one of my letters of rec in there until some time in November. There are a few places with 11/1 or 11/15 deadlines, which you may miss if you don't apply early. I can tell you that I got an interview invite from a place where I'd miss the dealine for "completed application" (though the only thing missing was 1 LOR). However, I wouldn't count on it...I would suggest NOT missing any deadlines. I don't see an advantage to delaying sending the CAF, unless you are awaiting something like your Step 3 score or a publication to be published, etc.
There are programs that will take applications in January, but most start reviewing them some time after 12/1.