The level of violent crime and homicides in Quebec is far lower than almost all other large cities in Canada or the USA.
For twenty months, between November 1st 2006 and July 14th 2008, the city of Québec reported no homicide on its territory.
During the day, you should have no fear about traveling around the city; but at night, there might be the usual drunk bar patrons and those who prey on people unfamiliar with where they are. Take the usual precautions to protect yourself and you should be fine. However, the city is very safe for solitary female travellers.
contact
The organization ZAP Québec (http://www.zapquebec.org) provides free wireless Internet in cafes and other locations throughout the city.