Moller played in bands including Meth O.D. and The Wow Kafe. His first solo work was 2003's "Maximum Smile".[3] He has collaborated with Stevie Jackson from Belle and Sebastian[4][5][6] in a band called the Store Keys.[7] He played with Davy Henderson in the band Jesus, Baby![3] When Marc Riley interviewed him on BBC Radio in 2011, he called Moller "Scotland's best-kept secret".[8]
In 2008, Moller had a son with wife Emma, named Peter.[9] In 2013, Moller moved to Dunbar.[4] In 2014 he took My Week Beats Your Year, his musical tribute to Lou Reed, to the Edinburgh Festival Fringe;[10] Gus Ironside called it "witty, mesmerising and highly poignant".[11] In the same year his poetry debut Imports was published by Appletree Writers Press,[12] and his album One Domino was called "intoxicating and compulsively habit-forming".[13]
Moller has been involved in the Dunbar CoastWord Festival,[14] and with Neu!Reekie![3][5] He contributed a poem to The Sea, a 2015 anthology to raise funds for the Royal National Lifeboat Institution.[15]Louder Than War called There's A Thousand Untold Stories (2016) "a tour de force of sparkling lo-fi gems".[16] In 2017 he performed Redemptions, an evening of poetry and song, with Paul Hullah and Martin Metcalfe, at the Scottish Poetry Library.[17]
In 2019, Dionysia Press published Moller's poetry collection about his birth and adoption, "Be My Baby" [18] Later that year, he returned to music, by releasing a single, Semicolon with the Chain Pier Group.[19]