A month before your visa expires, you should apply to change your status to visitor, see
http://www.cic.gc.ca/english/visit/extend-stay.asp Right now, the processing of that is taking 103 days, see
http://www.cic.gc.ca/english/information/times/canada/process-in.asp#temp_res so even if they refuse, you will at least buy some time. You should also talk to EI and find out about maternity benefits which you should have the right to start collecting at some point before the birth.