The 20-year-old, dressed in a headscarf, showed no ill affects from Friday night's opening ceremony when she carried the flag of the tiny Gulf nation, but her efforts ended at the first hurdle as she missed out on one of the eight places in the final.
Al Hamad finished with a score of 395 out of 400 from her 40 shots with 397 proving the required mark to compete for the first gold medal of the Games in a final which starts at 11:00am local time.
Swamped by requests for interviews the diminutive shooter appeared overawed by all the attention.
"Yes, I am very happy. I'm so proud," she told reporters before fleeing the media scrum that surrounding her.
Qatar, along with Saudi Arabia and Brunei, were the only IOC countries to have never sent a female competitor to the Olympics but all have women participating in London.
Al Hamad, who received a wild card to take part, is not the only woman competing for Qatar in London. Sprinter Noor Al-Malki and swimmer Nada Arakji will represent the nation which failed in a bid to host the 2020 Olympics but plans to try again for 2024.
Interest in the eight finalists at the Royal Artillery Barracks was limited as Malaysia's Nur Suryani Mohamed Taibi, who is eight months pregnant, stole the show.
Suryani said she had experienced three or four kicks during the 75 minute qualifying session. She finished 34th with a total of 392 from her 40 shots.
"I just breathed in and breathed out," she told reporters when asked if the kicks from her unborn child had put her off.
"I told her to behave herself, let mummy shoot, don't move so much. She always listens to me, luckily."
World number one Yi Siling of China and defending champion Katerina Emmons of the Czech Republic were amongst the eight women competing in the final which was attended by International Olympic Committee President Jacques Rogge.