Kocábová received her initial exposure at the age of eleven by providing early vocals for low-budget albums by Dagmar Patrasová, Baby studio s Dádou (1995) and Vánoce s Dádou (1996), both designed for children. Shortly before launching her debut set, she was given a credit as a co-writer on a track entitled "Some People" that appeared on album Velvet Revolution (1999), associated with Michael Kocáb, Petr Kolář and Tomáš Kympl. Her debut output Fly Apple Pie arrived on January 9, 2000, through Epic Records in partnership with Sony BMG. As the first full-length record issued by a Czech artist in the third millennium, it featured fifteen mainly English-sung tracks entirely crafted by her father Kocáb, whose name also appeared on the cover. Her mother, Marsha, supplied lyrics for a change. Upon its release, the album spawned a wide range of backlash from critics who slammed the entire work, commonly referring to as a shallow marketing tactic of Kocáb and accusing his daughter of nepotism, respectively. Despite two produced music videos, "So Changes Go" and "Mayday", the constant negative publicity hurt the album's sales.
Following years — in order to distance herself from further charges —, Kocábová had rather focused on writing her own poems and/or short novels. Her subsequent literary works, such as Slyšíš mě? (2002), Monarcha Absint (2003), Schola Alternativa (2004) and Někdo je v domě (2005), they altogether helped established her as an independent writer. Some of her side projects included music productions, though. For instance, she was cast in musical theatre Starci na chmelu (2001/02), while vocally she also contributed on her own father's act Za kyslík (2002). Her sophomore studio effort, Hummingbirds in Iceland, was launched on June 12, 2006. As with her previous release, the record was distributed via Sony BMG and supervised by Kocáb. Nevertheless, this time around she sought to work also with other songwriters-producers. Amongs other, with Michal Pavlíček Jr, Michaela Poláková and Lukáš Máchal. The album promoted by only video, "Neverland", received favorable feedback from journalists who acknowledged especially its progressive sound; only few reprised bias. But neither her second attempt would set charts on fire.
After two more or less fallow years, during which she published novel called Růže: Cesta za světlem... (2007), Kocábová began to take more initiative with her music, as well infused additional genres into her work. In 2008, she delivered the opening song "Tramtárie" for female compilation Ohrožený druh by Michal Horáček, also on Sony BMG. Starting 2009, singer gradually began collecting material that would serve as her most recent studio album. However, Walking on the A-bomb produced under the guidance of Jiří Burian, was rejected by Sony label. After Kocábová signed a distribution deal with music magazine Report, the result saw its eventual release in cardboard sleeve on December 1, 2010. Her third set, preceded by an EP of the same name, was well received on the indie club circuit and singer embarked on a tour in small venues.
Fifteen track album sung in English with exception of "ABC", "Kapka lásky and the final song "Duch Tarantina" that was in addition attached to Kocáb's double retrospective collection Best Of (2008), issued on Daranus.
Four tracks recorded during the Za kyslík album sessions for Kocáb, released on CD by Columbia. (In addition, "Urnovej háj" also appeared on second disc of the Kocáb's greatest hits compilation Best Of: Noční vyprávění o mé cestě od kostelní židle až k Pražskému výběru II (2008), issued on Daranus.)
D^ topped at number 1 on the Czech Albums Chart. The set became the most selling album of a music band in the Czech Republic with the sale of 22,766 copies. As of 2011, its total sale reached 35,000 units, while being certified with double platinum from ČNS IFPI. In addition, the work won the Anděl Award as the Album of the Year.