Advancing the Quality and Understanding of American Aquaculture Act or the AQUAA Act This bill establishes standards for sustainable aquaculture in federal offshore waters in the exclusive economic zone and establishes related requirements. For example, it requires the National Oceanic and Atmospheric Administration (NOAA) to establish a national plan to identify and designate aquaculture opportunity areas. In addition, NOAA must establish a unified permitting and review process for aquaculture operations. NOAA must also establish a grant program for research and development to support the development of a sustainable marine aquaculture industry, such as research and services to create innovative design and engineering solutions to common obstacles within the aquaculture industry. Finally, the bill directs the Department of Commerce to create and provide resources for an Office of Aquaculture within NOAA to coordinate regulatory, scientific, outreach, and international issues related to aquaculture.