Al Hamad, 19, will compete in the 10M competition. She had won three gold and two silver medals at the 2011 Arab Games in Doha.
International Olympic Committee had given wild card to sprinter Noor Al Malki and swimmer Nada Arkaji.
Qatar, Saudi Arabia and Brunei have never before sent women athletes to an Olympics although the Saudis are in discussions with the IOC.
Qatar is bidding to host the 2020 Games, along with Madrid, Tokyo, Istanbul and Azerbaijan capital Baku.