Randomized phase II trial to study the effectiveness of chemotherapy with paclitaxel and the monoclonal antibody trastuzumab followed by chemotherapy in treating women who have stage II or stage IIIA breast cancer that overexpresses HER2. Drugs used in chemotherapy use different ways to stop tumor cells from dividing so they stop growing or die. Monoclonal antibodies can locate tumor cells and deliver tumor-killing substances to them without harming normal cells. Combining monoclonal antibody therapy with chemotherapy may kill more tumor cells.