Career
A Charlton Athletic youth graduate, Muldoon signed a new deal with the club on 6 December 2013, running until the end of the campaign. He was an unused substitute for the matches against Blackburn Rovers and Brighton & Hove Albion in January 2015. On 11 March 2015 Muldoon agreed a new deal with the Addicks, signing until 2017 and being immediately loaned to Gillingham until the end of the season.
He made his professional debut three days later, starting in a 0–0 away draw against Bristol City in League One.
In January 2016, he signed for Football League Two side Dagenham & Redbridge on loan until the end of the season.