Dobbs attended the University of Tennessee where he appeared in 37 games (35 starts) and completed 614-of-999 passing attempts (61.0%) for 7,138 yards and 53 touchdowns in addition to 438 carries for 2,160 yards and 32 touchdowns. During his collegiate career, Dobbs was named the 2016 AP Second-Team All-SEC recipient. He was drafted by the Pittsburgh Steelers in the fourth round (135th overall) of the 2017 NFL Draft.
Throughout Dobbs' seven-year career with the Steelers (2017-21), Tennessee Titans (2022), Arizona Cardinals (2023) and Minnesota Vikings (2023) he has appeared in 21 games (14 starts) and completed 312 of 502 passing attempts (62.2%) for 2,920 yards and 15 touchdowns. In 2023, Dobbs appeared in a career-high 13 games (12 starts) and completed 262-of-417 passing attempts (62.8%) for 2,464 yards and 13 touchdowns between his time in Arizona and Minnesota.