This pilot clinical trial studies how well copper Cu64-DOTA-trastuzumab positron emission tomography (PET) works in predicting response to treatment with trastuzumab and pertuzumab before surgery in patients with human epidermal growth factor receptor 2 (HER2) positive breast cancer that has spread from where it started to nearby tissue or lymph nodes. Diagnostic procedures, such as copper Cu 64 DOTA-trastuzumab PET, may help predict a patient's response to trastuzumab and pertuzumab before surgery in patients with locally advanced HER2 positive breast cancer.