Our party of 6 were based in Jerusalem we were there for 9 days. Very convenient for traveling around. Stayed in Yemi Moshe area just outside the old city walls. In November (2012) you could not take a hire car out of Israel. See my various posts for Israel.
Yes I would suggest two days for Petra. Lots of places to ask for travel guidance. Look at the temperature, it can get hot, even in November we always had water with us.