Dobbins has received commissions from the Koussevitzky Foundation, the Saint Paul Chamber Orchestra, The Fromm Foundation, and the Pro Arte Chamber Orchestra of Boston. Fellowships and awards include the Lili Boulanger award from the National Women Composers Resource Center; the Goddard Lieberson Fellowship from the American Academy and Institute of Arts and Letters; ASCAP Special Award for Composition; First and Second prizes in the International League of Women Composers Composition Contest; residencies at the MacDowell Colony and the Atlantic Center for the Arts; Composers Conference at Wellesley College Fellowship; grants from Meet the Composer; and several awards from UC Berkeley for her work in composition.

Her works have been performed by the Pro Arte Chamber Orchestra of Boston, the Saint Paul Chamber Orchestra, Collage, New Music Consort, New Jersey Percussion Ensemble, San Francisco Contemporary Music Players, Earplay, Composers Forum, North/South Consonance, Berkeley Contemporary Chamber Players, Women's Philharmonic, Brandeis Contemporary Chamber Players, Minnesota Composers Forum, at the 14th Annual New Music & Art Festival at Bowling Green State University, Piccolo Spoleto Festival, Cal Arts New Music Festival, Seattle Spring Festival, and the Society of Composers Inc./Florida State University New Music Festival. Her composition for chamber orchestra, Fire and Ice, has been released by Vienna Modern Masters (VMM 3018). Several of her works are published by Margun Music and G. Schirmer, Inc.