A search in the Quebec section for Gens de Terre will give you a few pointers.
The water level is regulated via a Dam. It is usually early in the season that you may see rather high water levels. All depends on the water level in the network of reservoirs in the area and the spring run off. Please take note that early in the season you have to take into account the added impact of the river watershed flowage. A 50 m3/s at Barrage Cabonga in May means a higher level than 50 m3/s in August in the Canyon.
If you want to abide by the rules, you will need to wait for the opening of the canoeing season in the Reserve faunique de la Verandrye which is May 17th. You can still ask the SEPAQ if they agree to let you go bypassing CCLV regulations. Besides, the shuttle service from CCLV can be an asset unless you drive a 4X4. Even if regular shuttle service starts on June 9th, you can make a special agreement before.
CCVL is also the best source to get the water level at Barrage Cabonga. They also advise Hydro Quebec that a party is on the river in order to hold further increase in water level.
The map from
http://www.cartespleinair.org is a must since the CCVL map is not up to date and displays portages long overgrown. This is not an inviting river for guess work.