It depends on the route that you choose. We did a loop trip from Nym Lake to Quetico Lake: 13 portages, total portage distance 5818 m., longest portage 1120 m., average portage length 447 m.
Unlike other parks such as Algonquin, the park map does not show portages or campsites. Your best bet for trip planning is to go to Paddle Planner at
https://www.paddleplanner.com/tools/maps/bwcaqueticomap.aspx where you will find an interactive map giving campsites, portages, distances, and estimated travel times. Once you have decided on a route, purchase the appropriate 1:50,000 topographic maps.
You can find a bit of additional information in Kevin Callan's "A Paddler's Guide to Quetico and Beyond" and from the Canadian Canoe Routes website; otherwise information is pretty scarce. Camp Quetico resort near Atikokan seems to have a lot of canoeists going through and could very likely provide information and tips (807-929-2266).
Most portages were in good shape but I think that you would have some difficulty trailering a kayak and gear; the trails are good but not that good!
13 days in Quetico Provincial Park, and the fishin' is easy
