This is one of the classic Canadian canoe trips, and gets a lot of visitors in high season. The best time to visit is the spring, before the bugs and crowds have arrived. You will have many more options for campsites, and spring flows will speed you along.
Your journey starts with a paddle along the length of lake Traverse, so take a fast boat. There are campsites aplenty, but the only drinking water source is a spring near the far end of the lake on the right bank. The rapids start soon after, interspersed with lake crossings. Everything is fairly easy until Crooked Chute. There are plenty of warning signs, portage on the right bank if needed. At high water this will be a stout proposition.
A while after, the scenery gets even better, but the whitewater diminishes. Soon you will find yourself on a series of linked lakes towards the end of the section. Make sure that you do not go past the take out - there is an active artillery range downstream!
To get to the take out; First check that you have enough gas for 200 km of driving! Then from highway 17, turn south onto Doran road (about 6 km south-west of Petawawa). Almost immediately, turn right onto Barron Canyon road. This leads to the Sand lake gate to Algonquin Park. Stop and book your campsites if you have not already done so, and maybe ask about the road conditions. Continue on Barron Canyon road, turning right onto McManus Lake road. The take out is at the end of the road. The park map here might be useful.
To get to the put in; Return to Barron Canyon road and turn right. This turns into Lake Travers road. The put in is after the 71 km marker, at the bridge over the Petawawa as it enters lake Traverse.