It is safe to eat brown grouper while you are pregnant, but you should limit the amount of consumption due to concern of mercury in the brown grouper.
Brown snapper is lean source of protein and it contains omega-3 fatty acids, vitamin A as well as selenium which are beneficial.
Omega-3 fatty acids are good for the brain development of the fetus. Iron present in grouper is important for red blood cell formation. This can help to prevent anemia during pregnancy.
However, due to pollution, there is mercury found in the brown grouper. Presence of mercury in the pregnant women has been found to be related to some birth defects and this heavy metal usuaully will stay in the body for quite long.
Therefore, you should limit the consumption to one or two times in a month.