Advancing the Quality and Understanding of American Aquaculture Act or the AQUAA Act This bill directs the Department of Commerce to establish an Office of Marine Aquaculture within the National Oceanic and Atmospheric Administration to coordinate regulatory, scientific, outreach, and international issues related to aquaculture. Commerce must establish a research and development program to award competitive, peer-reviewed grants to fund research and extension services, including to develop and evaluate methodologies to prevent, minimize, and mitigate potential adverse ecosystem and socioeconomic impacts of marine aquaculture.