Al-Hamad, 19, will compete in the 10 metres competition after winning a silver medal in the team event at the Arab shooting championships last month. She was Qatar's most successful athlete at the 2011 Arab Games in Doha with three gold medals and two silver.
She joins swimmer Mohammed Wafa Arakji and 100 and 200 metres sprinter Noor Al-Malki in the Qatar team.
"We are absolutely delighted that we have been able to secure another place for one of our young female athletes at London 2012," Qatar Olympic Committee general secretary Sheikh Saoud bin Abdulrahman Al-Thani said in a statement.
"We are grateful to the IOC for their support in helping make this happen.
"Athletes like Bahia, Nada and Noor will also provide inspiration to the next generation of female Qatari sports."
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.
As part of its bid Qatar plans to build a high-performance training centre for female athletes in Doha.