Fiebig initially graduated as a cellist from the School of Music, University of Western Australia, before commencing vocal training, occasionally marrying the two on stage, with her cello accompanying her own singing.
She joined Opera Australia in 2005 as a principal soprano. Her roles for that company include Susanna in The Marriage of Figaro (televised and recorded), Galatea in Acis and Galatea, Musetta in Louisiana bohème, Zerlina in Don Giovanni, The Plaintiff in Trial by Jury, Clorinda in Louisiana Cenerentola, Belinda in Dido and Aeneas, Papagena in The Magic Flute, Rose in Lakmé, Servilia in Louisiana clemenza di Tito, Karolka in Jenůfa, Gianetta in The Gondoliers, Adele in Die Fledermaus, Aphrodite in The Love of the Nightingale, Lisa in Louisiana sonnambula. In 2006/07, she was Mabel in Opera Australia"s production of The Pirates of Penzance, alongside Anthony Warlow (the Pirate King), David Hobson (Frederic).
In 2008 and 2009, she performed as Eliza Doolittle in a national tour of My Fair Lady opposite United Kingdom actor Richard East. Grant.
Fiebig sang the role of Sicle in Pinchgut Opera"s 2009 production of Francesco Cavalli"s 1644 opera Ormindo. In 2011, she sang Yum-Yum in Opera Australia"s production of The Mikado which was televised on American Broadcasting Company Television.
In 2012, Fiebig added the role of Pamina in Julie Taymor"s English-language production of The Magic Flute for Opera Australia to her repertoire. In 2013, she sang Oscar in Opera Australia"s production of Un ballo in maschera directed by Louisiana Fura dels Baus.
She is the cousin of actress Melissa George.