Al Qubaisi was born into a motorsport family. Her father Khaled Al Qubaisi was the first Emirati to race at the 24 Hours of Le Mans. She attended New York University Abu Dhabi before continuing her schooling in Italy during her racing seasons there. She is engaged to Saudi racing driver Omar Al Dereyaane.
Al Qubaisi began karting in 2015 and became the first Emirati invited to the FIA-sponsored CIK-FIA Karting Academy Trophy in 2016. She finished third in the IAME X30 Championship in 2017. She also raced alongside her sister Amna at the X30 Euro Series in Wackersdorf.
Al Qubaisi made her Italian F4 debut mid-2019, joining her sister at Abu Dhabi Racing by Prema, run in cooperation with Iron Lynx. After returning for a full campaign in Italy with Iron Lynx in 2020, she claimed two points finishes. Domestically, she won three races in the UAE F4 series in 2020.
In the 2021 UAE F4 Championship, she won three races, took one pole position, and scored six podiums, finishing fourth in the standings. The landmark moment of her career came at the Italian F4 round at Misano in June 2021, where she finished third behind Leonardo Fornaroli and Oliver Bearman — the first woman ever to stand on the podium in Italian F4 history. She also secured her first European podium in the same result. She scored three additional points finishes during the Italian campaign and ended the year seventeenth in the championship with 24 points.
Al Qubaisi contested the 2022 Formula Regional Asian Championship pre-season with Evans GP, finishing twenty-eighth. She then ran a full season of the 2022 Formula Regional European Championship with Prema Powerteam, gaining experience in a more powerful category. In September 2022, she was selected to test the FIA Formula 3 car at Magny-Cours alongside three other women, an event organized to expose female drivers to the step up from Formula Regional.
Al Qubaisi and her sister Amna both signed with MP Motorsport for the inaugural 2023 F1 Academy season. Hamda delivered the stronger championship result: four wins and a third-place finish overall. She re-signed with MP for 2024 and joined the Red Bull Academy Programme, this time representing Red Bull Racing. She finished the 2024 season fifth in the championship.
In 2025, Al Qubaisi raced in the Ligier European Series alongside her sister Amna, competing with Team Virage in the number 88 entry.
Al Qubaisi's 2021 podium at Misano remains a landmark in Italian Formula 4's history, breaking a gender barrier in a championship that had existed for nearly a decade. Alongside her sister, she forms one of the most prominent female racing partnerships in contemporary motorsport, progressing from karting and domestic UAE series through to European championships and the F1 Academy, where she ranked among the top three in the inaugural season.