This phase II trial is studying the side effects and how well giving cyclophosphamide and paclitaxel with or without trastuzumab works in treating women with stage I or stage II breast cancer who have undergone surgery. Drugs used in chemotherapy, such as cyclophosphamide and paclitaxel, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Giving monoclonal antibody therapy, such as trastuzumab, with chemotherapy may kill more tumor cells. Giving these treatments after surgery may kill any tumor cells that remain after surgery