Known for his political comedy, he has appeared on Australian TV shows including Kath and Kim, Spicks and Specks, Good News Week, Stingers, Blue Heelers, MDA and The Sideshow. Perfect has released two solo albums; Welcome to the Inside of Ed's Head and Angry Eddie, the latter of which released after his appearance on the compilation Rock Against Howard. He also released an album with Tripod under the moniker of Perfect Tripod, entitled Australian Songs, in 2013.
In 2007, Perfect appeared in Keating! the Musical, playing several characters, including a parody of former Australian Minister for Foreign Affairs Alexander Downer. Also that year, Perfect wrote Shane Warne: The Musical, a satire based on the life and exploits of Australian test cricketer Shane Warne. It premiered at the Melbourne Athenaeum theatre on 10 December 2008 before embarking on a national tour. In 2009 the musical received the Helpmann Award for Best New Australian Work, the Green Room Award and the Victorian Premier’s Literary Award.
Perfect has appeared on The Little Dum Dum Club twice to date. His appearance came in the show's eighteenth episode, which was published on February 21st, 2011. He returned for the show's 120th episode alongside Josh Earl.