The motor does exert torque on the fuselage.
The pilot, without having to think about it, compensates by applying right aileron, which has plenty of roll authority.
There's more to it.
When a propeller-driven plane is taking off, it has a tendency to yaw to the left, and the pilot automatically applies right rudder to compensate.
That left-turning tendency is due to the propeller descending on the right hand side, at a higher angle of attack (thus more thrust) due to the pitch of the airframe, and also because the wind coming off the propeller is a corkscrew flow, and it strikes the left side of the vertical stabilizer.
If you watch this video, you will see how pilots are instructed to operate the F4U Corsair in WW2.
It is recommended to tune in some right-rudder and right-aileron trim when taking off.
It is also recommended not to take off at too slow a speed because it will seem "left-wing-heavy" due to that torque, and more speed means more control authority.