it takes a week or two to get your secondaries after your AMCAS, it takes another 4-6 weeks after your secondaries to get interview invites, and wait for a month or two weeks to actually interview. say you use a week to finish your secondary, it would be 3 months to attend an actual interview from the day you completed your primary. if you did it in October, the earliest interview would be in late January, at that time, private schools have already given out number of spots that are equivalent to their class size.
To answer your question, really, it is not too late. My primary was done a day before Nov 1st, rec letters got in before Christmas. all my secondaries were completed in the first two weeks of January. however, this limited the number of interviews to 3...therefore the chance of being accepted to the school of your choice is limited.