Palmer began his career as a youth at Brentford. His maiden call into the first team squad came for a Football League Trophy first round match against Milton Keynes Dons on 28 September 2004. Manager Martin Allen selected a side mostly composed of players from the youth team, including Ryan Peters, Sean Hillier, Josh Lennie, Karleigh Osborne, Darius Charles, Jamie Palmer and Scott Weight. Muldowney made his professional debut in the match, coming off the bench for Stephen Hunt at half time during the 3–0 defeat. Muldowney was called into the first team squad again on 30 October and was an unused substitute for a 1–0 defeat to Tranmere Rovers. It was Muldowney's final involvement for the first team and he was released in the summer of 2005, having made just one appearance for the club.
Muldowney and Brentford youth teammate Jamie Palmer joined Isthmian League Premier Division side Kingstonian on work experience loans in December 2004. Muldowney made his debut with a starting appearance in a 2–0 win over Yeading on 1 January 2005. He made six appearances for the club before returning to Griffin Park in March.
Muldowney and Jamie Palmer signed on loan for Isthmian League Premier Division side Staines Town in March 2005, until the end of the 2004–05 season. Muldowney made his debut with a start in a 2–1 defeat to Windsor & Eton on 19 March. He made only one more appearance for the club in a 2–0 defeat to Leyton on 2 April and returned to Brentford at the end of the season. After an unsuccessful trial at Championship side Reading, Muldowney signed for Staines permanently in the summer of 2005. Muldowney made his first appearance of the 2005–06 season in a 2–1 win over Margate on 23 August 2005. He managed only eight appearances for the Swans before departing in October.
Muldowney joined Isthmian League Division Two side Chertsey Town in October 2005. He made 18 appearances during the 2005–06 season and scored no goals. With the Curfews reassigned to the Combined Counties League Premier Division for the 2006–07 season, Muldowney was a virtual ever-present, making 49 appearances. He was in red hot goalscoring form in November and December 2006, bagging seven goals in 9 games. He ended the campaign with 9 goals.
Muldowney signed for Isthmian League Premier Division side Wealdstone in July 2007. He made his competitive debut for the club in a 4–1 win over Folkestone Invicta on 18 August 2007. Muldowney scored his first goal for the club in a 2–2 league draw with Heybridge Swifts on 25 September and scored again in the following game, bagging the winner in a FA Cup second qualifying round win over Carshalton Athletic. He made 23 appearances during the 2007–08 season, failing to establish himself in the side, with 10 of his appearances coming in cup competitions.
Muldowney returned to Chertsey Town on loan in December 2007, a move which was later turned into a permanent signing. He made 22 appearances during the 2007–08 season, scoring no goals. Muldowney made his first appearance of the 2008–09 season in a 6–0 thumping of Badshot Lea on 9 August 2008. He notched his first goal of the campaign in a 2–1 FA Cup qualifying extra preliminary round replay win over Deal Town on 19 August. He scored two goals in three games in September, helping the Curfews to a 3–2 win over Cove and a 6–0 thrashing of Hartley Wintney. Muldowney bagged his third goal of the season in a 6–4 Surrey Senior Cup third round win over Bookham on 20 January 2009. A broken toe disrupted the second half of his season, but Muldowney was denied the chance to win the first silverware of his career after Chertsey were removed from the Premier Challenge Cup Final, for fielding an ineligible player in their semi-final win over Worcester Park. Muldowney made 41 appearances during the 2008–09 season and scored four goals. He left the club in the summer of 2009.
Muldowney signed for Combined Counties League Premier Division side Egham Town in the summer of 2009. Muldowney's debut for the club came in a 1–1 draw with Horley Town on 8 August 2009. He scored his first Egham goal in a 4–3 win over Epsom & Ewell on 12 December. He struck again two games later, helping the Sarnies to a 4–2 win over Camberley Town. Muldowney's third goal of the season came in a 4–1 away win over Ash United on 10 April 2010. He had a first successful first season with Egham, making 41 appearances and scoring three goals as the Sarnies achieved a fourth-place finish in the league. After a mediocre 2010–11 season which saw the Sarnies finish 13th (though Muldowney improved his goal tally to four), they made a challenge for the title in the 2011–12 season, with Muldowney making 39 appearances. He scored his first goal of the season in a 7–1 rout of Cove on 29 October 2011. He put in a man of the match performance in a 3–2 win over Croydon on 12 November, scoring the winner at the start of the second half. Muldowney accrued two more man of the match awards during the season, for his performances in wins over Horley Town and Guildford City in March 2012. Everything came right for Egham Town in the 2012–13 season, with Muldowney making 45 appearances and scoring five goals on the way to the Combined Counties League Premier Division title. The winning goal and the man of the match award in the final day victory over Bedfont Sports capped Muldowney's season. Muldowney began life in the Southern League Division One Central well, scoring in a 3–0 away win over Aylesbury on 24 August 2013. He made 40 appearances and scored two goals during a mid-table 2013–14 season, dropping to 24 appearances and one goal in 2014–15 and departing in February 2015.
Muldowney joined Combined Counties League Premier Division club Hanworth Villa during the 2014–15 season.
In October 2014, Muldowney was named as player-manager of Southern League Division One Central club Egham Town. He remained in charge until being replaced by Koo Dumbuya in February 2015.
Muldowney was named as assistant manager at Combined Counties League Premier Division in 2015. He and the entire management team stepped down after the club's Middlesex Senior Cup win at the end of the season.
Muldowney linked up with former Brentford youth teammates Mark Scotchford, Barry Marchena and brother Charlie Muldowney to make seven appearances for West Middlesex Sunday Football League side Green Man Rangers in 2011.
Muldowney's brother Charlie was also a product of the Centre of Excellence at Brentford. He never made a first team appearance and is a personal trainer. His other brother, Jamie, also played for Brentford he signed a two-year apprenticeship in 1997 he played for the youth team and reserves in that time and played for a hoist of non-league clubs Fisher Athletic, Greenwich Borough and Egham town the brothers were teammates at Chertsey Town during the 2000s.
Egham TownCombined Counties League Premier Division: 2012–13