As a junior, Moller played football for the Cronulla Sharks Junior Australian Football Club and was part of basketball's national junior development program and considered a future NBL player capable of representing Australia. He played football and basketball at both Lucas Heights Community School and Sydney Boys High School. At age 14, the Fremantle Football Club began developing Moller via the New South Wales AFL Scholarship Scheme. Joining Fremantle on a three-year scholarship, Moller travelled to Fremantle twice a year and went on three training trips to Melbourne. At the under-16 level, he began playing for the Sydney University Australian National Football Club in the North East Australian Football League, and in 2012, he spent part of the season playing for the GWS reserves. In December 2012, he was officially drafted by Fremantle in the 2013 rookie draft. After spending most of the 2013 season playing for Peel Thunder in the West Australian Football League, Moller was elevated to the Fremantle senior list prior to the final round of the 2013 AFL season for the team's game against St Kilda at Etihad Stadium. He was then a late inclusion in the side as the substitute player when many senior players were rested ahead of the finals. Moller continued on with Fremantle in 2014 and 2015, but did not manage another AFL game, playing out both seasons in the WAFL with Peel Thunder. Following the conclusion of the 2015 AFL season, Moller was delisted by Fremantle.
In early January 2016, Moller began training with the National Basketball League's Sydney Kings. He and fellow Australian centre Jordan Vandenberg were brought in for tryouts by the Kings as potential injury replacements for Julian Khazzouh. Moller ultimately lost to Vandenberg for the spot but stayed on with the team as a full-time training squad member. With an injury to back-up forward Jeromie Hill in early February, Moller was elevated to the Kings' playing roster for their match against the Perth Wildcats in Sydney on 10 February, the second last game of the Kings' 2015–16 season. He made his NBL debut in that game, entering the contest for the final one minute and 47 seconds of the last quarter. In March 2016, Moller joined the Sutherland Sharks for the start of the 2016 Waratah League season. On 22 April 2016, after averaging 19 points and 11 rebounds in six games for Sutherland, Moller signed a short-term deal with the Ballarat Miners of the South East Australian Basketball League. He was retained by the Miners for another month on June 16. In 13 games for the Miners, Moller averaged 10.3 points, 9.7 rebounds and 1.9 assists per game. On 21 September 2016, Moller signed with the Sydney Kings as a development player for the 2016–17 NBL season. In the Kings' season opener on 8 October 2016, Moller played 13½ minutes off the bench and recorded four rebounds and one assist in a 77–73 loss to the Brisbane Bullets. Moller was promoted to the full-time team midway through the season following the departure of American import Steve Blake. He appeared in 13 games for the Kings in 2016–17, averaging 3.3 points and 2.3 rebounds per game. On 23 November 2016, Moller re-signed with the Ballarat Miners for the 2017 SEABL season. On 11 April 2017, he was named SEABL Player of the Week for Round 3. On 19 June 2017, he was named SEABL Player of the Week for Round 11. In 22 games for the Miners, Moller averaged 17.7 points, 10.8 rebounds and 3.0 assists per game. On 13 April 2017, Moller signed a three-year deal with Melbourne United. In March 2018, he helped Melbourne win the NBL Championship. On 5 January 2018, Moller signed with the Hobart Chargers for the 2018 SEABL season. On 25 May 2018, he recorded 43 points and 15 rebounds in a 95–86 win over the Ballarat Miners. He was subsequently named SEABL Player of the Week for Round 8. In August 2018, he helped the Chargers win the SEABL Championship. In 23 games, he averaged 23.2 points, 12.1 rebounds, 3.0 assists and 1.2 steals per game. In November 2018, Moller was called-up to the Australian Boomers squad for the team's next window of 2019 FIBA World Cup qualifiers. The 2018–19 NBL season saw Moller appear in all 34 games for United, helping them reach the grand final for a second straight year. He averaged 3.9 points and 2.7 rebounds per game. Following the season, he joined the Southern Huskies for their debut season in the New Zealand NBL. On 15 April 2019, Moller signed a two-year deal with Sydney Kings, returning to the team for a second stint. He appeared in the first 11 games of the 2019–20 season before missing the next 16 games with a right ankle injury. He returned for the Kings' final regular season game.
