Doohan began karting in 2012, winning Australian national titles before moving to Europe. He started single-seater racing in the F4 British Championship in 2018, then competed in the F3 Asian Championship and Euroformula Open before joining the FIA Formula 3 Championship with HWA Racelab in 2020. That debut F3 season was difficult, yielding no points, but a switch to Trident in 2021 transformed his fortunes. Doohan finished runner-up to Dennis Hauger in that 2021 FIA F3 championship, with victories at Spa-Francorchamps including the notable distinction of becoming the first F3 driver to score two wins on the same weekend. A member of the Red Bull Junior Team until 2021, he left the programme and joined the Alpine Academy in 2022.
Doohan stepped up to Formula 2 with Virtuosi Racing for a partial campaign at the end of 2021 (two rounds, 19th overall), then contested a full 2022 season. His year was a study in consistent speed mixed with mechanical and strategic misfortune. He claimed pole position at the season opener in Bahrain but was removed from contention by a pit-lane collision with Theo Pourchaire. Disqualifications in Jeddah and incidents at Imola and Baku marked an early campaign of squandered potential.
The second half of 2022 showed what Doohan was capable of. He won his first Formula 2 feature race at Spa-Francorchamps, undercutting championship leader Felipe Drugovich during the pit stop phase and holding on for victory. He had earlier won the Silverstone sprint race in wet conditions, threading his way to the front with composed overtaking. A second sprint victory came at Budapest. He claimed a further podium at the Red Bull Ring. Bad luck returned in the final rounds: a loose wheel at Yas Marina cost him a likely points finish in the penultimate race. He ended the season sixth in the drivers' standings with 128 points, three wins, three pole positions, and six podiums.
Doohan remained with Virtuosi for 2023, partnering Amaury Cordeel. The season followed a similar arc — patchy early form giving way to a strong second half. A disastrous Bahrain opener and a spin in Saudi Arabia left him outside the top ten in the standings at the midpoint, but results improved sharply.
In Hungary, Doohan took pole position and dominated the feature race, winning by nine seconds. The following round at Spa-Francorchamps saw consecutive feature race wins: he came through on alternate strategy when a late safety car deployed, passed Theo Pourchaire on the penultimate lap, and won. His end-of-season form culminated in a pole and victory at the Yas Marina finale, where he controlled the race from the front and pipped Ayumu Iwasa for third in the final standings. Doohan ended 2023 with three wins, five podiums, and two pole positions, jumping Iwasa in the drivers' championship at the final round.
He received the inaugural Formula 2 Best Performance Award at the end-of-season ceremony, sharing it with Richard Verschoor.
Doohan's two Formula 2 seasons with Virtuosi, bookended by consistent improvement, were sufficient to secure his Alpine seat. He had already served as Alpine's reserve driver in 2023 and 2024 with multiple free practice appearances at Mexico City and Abu Dhabi. He made his race debut for Alpine at the 2024 Abu Dhabi Grand Prix as a replacement for departing Esteban Ocon, then joined the team full-time for 2025 alongside Pierre Gasly. His Formula One stint was cut short after six rounds without points; he was replaced mid-season by Franco Colapinto. Doohan subsequently moved to Haas as reserve driver and joined Nielsen Racing for the 2026 European Le Mans Series in the LMP2 class.