 This phase II trial studies the side effects and how well cyclophosphamide, paclitaxel, and trastuzumab work when given after surgery in treating patients with stage I-II human epidermal growth factor receptor HER2neu positive breast cancer confined to the breast or the breast and lymph nodes under the arm. 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, by stopping them from dividing, or by stopping them from spreading. Monoclonal antibodies, such as trastuzumab, may interfere with the ability of tumor cells to grow and spread. Giving cyclophosphamide, paclitaxel and trastuzumab after surgery may help prevent the cancer from coming back. 