LIke Fred said I would strongly suggest a larger 2-1/2 HP router at a minimum. If for no other reason that becasue you will need a 1/2 inch style collet to hold a decent router bit to cut your 2 sides. That’s the other thing you will be cutting 2 sides on your planks to do this. I honestly thought of something similar years ago for bench and bought a set.
What I ended up doing - was biscuit joints. Why - supposedly just as strong once glued right, more forgiving for the setup. Now I’ve made another bench (sitting bench not work bench by the way) and that time I did dado setup on the table saw. Worked well.
Meanwhile if buying a mid size router as they are called I would point you either to the Bosch 1617EV that is still out there. The updated Bosch whose number I forget at the moment. Or the Dewalt I think it’s a 618 which is the larger of that set. I’m always looked at either of those but haven’t bought one yet.