Quite confusingly, this trail is know in English as the IAT-QC (International Appalachian Trail in Québec) or in French as the SIA-QC (Sentier International des Appalaches au Québec). In addition, the trail is know by a third acronym – the GR-A1 – using the European technique for naming hiking trails with numbers preceded with GR (Grande Randonnée in French, Grote Routepaden in Dutch, Grande Rota in Portuguese or Gran Recorrido in Spanish). For simplicity, I’ll refer to it as the IAT in Québec.
After leaving New Brunswick, the IAT in Québec crosses over hills and valleys from south to north on the Gaspé Peninsula. Upon reaching a large wildlife reserve followed by a Québec provincial park, it turns east to climb the Chic-Chocs Mountains. It continues on the peaks of the Chic-Chocs east until leaving the park, then again turns north, leaving the mountains and heading for the coast. It follows the coast east until reaching the end of the peninsula at a National Park and the Atlantic Ocean. Depending on the source, the IAT in Québec is said to cover from 600 to 650km, with the GPS files as of fall 2016 giving a total of somewhere around 640km.
Note that the association of the IAT in Québec seem to have generously made an effort to include info online for non-French speakers. The English site at this time however seems to be incomplete and little more than a machine translated version. As such, a browser installed plug-in for Google Translate with the French language site will likely give a more complete experience.