Is praying four rak'ahs for the Sunnah prayer before Dhuhr (the midday prayer) with one tashahhud and sujood as-sahw (prostration of forgetfulness) correct, or should it be prayed two rak'ahs by two rak'ahs?

What you did is correct according to the Maliki school. Whoever prays two supererogatory rak'ahs, then inadvertently stands for a third and formalizes it by raising his head from its bowing (ruku'), he completes what he is doing as four rak'ahs, except for the Fajr prayer. According to the Shafi'i school, the regular supererogatory prayer before Dhuhr is valid as four rak'ahs with one taslim and one tashahhud if that was intended at the time of the opening takbir; otherwise, the addition is not permissible. It is preferable for it to be with two taslims.