Incorporation isn't required, but delaying equity agreement is a recipe for a painful co-founder breakup later when it emerges that I thought we were going in 50/50 and you thought it was 70/30.
You should at least have talked about all the points that go into an incorporation document and some that don't (equity shares, vesting, time & work commitments, decision-making, roles, etc.) and have a verbal agreement that everyone's on-board with. You don't have to actually file the paperwork, which is expensive and creates ongoing administrative work. You should file the paperwork ASAP, but if a founder starts working on the project and then decides that his true desires lie elsewhere or he's not happy with the working arrangement, that's often easier to fix before there's a real company than afterwards.