[1] Baastrup has a career as a civil servant and in the trade union movement.

She was employed as a clerk in the Local Government Association from 1976 until 1980, when she moved to a position in the Danish Parliament as committee secretary.

[1] As chairman of the Legal Affairs Committee, she was responsible for the appointment of former Attorney General Jørgen Steen Sørensen, as the new Ombudsman, replacing Hans Gammeltoft Hansen.

In May 2008, in a ballot against mayor Bo Asmus Kjeldgaard, she lost the battle to become the party's lead candidate in Copenhagen Municipality.

[3] Baastrup lists "growth, jobs and education", "public transport" and "people with disabilities" as her key issue.