You will not have to pick up your bag at YYZ on a domestic - transborder connection in Terminal 1. However, you will have to wait in a special transit hold area until your name appears on a screen (i.e. your bag has been matched in the bowels of YYZ) before you can proceed to customs and through security again.
1h20min is not impossible but tight, especially if you don't have Nexus / Global Entry for the US.