Your doctor is correct. Based on NCNN guidelines any tumor less than or equal to 0.5 cm does not require any further treatment after surgery. Unless, you had lymph node involvement then you should consider adjuvant chemotherapy.
My tumor was 2.2 cm so I had surgery, chemo, followed by radiation. Treatments can vary based on the size of the tumor, lymph node involvement, type of surgery, biopsy results, and your age. It is very difficult to compare treatment plans since no two people are alike. It is better to verify that your physician is following national comprehensive cancer network guidelines which should assure you that you are receiving the correct treatment.
Wishing you all the best,
Diane