*Club domestic league appearances and goals, correct as of 18:38, 12 June 2024 (UTC) ‡ National team caps and goals, correct as of 13:32, 19 June 2020 (UTC)
Mooney is a product of the Fleetwood Town Academy. At the beginning of the 2017–18 season he was sent out on loan to Northern Premier League Division One North side Bamber Bridge, where he was in excellent form as the side made a fine start to the season.[3] He left the club in December 2017, subsequently signing a one-month youth loan for National League North side Chorley, having impressed manager, Matt Jansen, when playing against the Magpies for Bamber Bridge in the Lancashire FA Challenge Trophy quarter-final.[3] In February 2018, he signed for Northern Premier League Premier Division side Ashton United on loan.[4] On 9 October 2018 Mooney made his debut for Fleetwood in the starting line up for a 2–0 defeat against Rochdale in the EFL Trophy.[5] In May 2019 Mooney signed a one-year contract extension with Fleetwood.[6]
On 4 January 2020, it was announced Mooney had joined National League North side Altrincham for an undisclosed fee.[7] He made his debut the same day, starting in a 5–2 win against Telford.[8]
Mooney joined Southend United on 26 May 2022. "Dan has obvious qualities," said Blues Head Coach Kevin Maher.[9] He left the club in December 2023 after his contract was cancelled by mutual consent, and rejoined former club Altrincham.[10] He departed Altrincham at the end of the 2023–24 season.[11]
In June 2024, Mooney joined newly promoted National League club Boston United.[12]