Terezi could be considered Karkat's counterpoint in many ways; most notably, her voice. She's got a nasally, raspy sort of sound-many voice actors do it differently, and its going to be challenging to balance that with /singing/, so good luck!

As far as her singing voice itself, I'd classify Terezi as a "mezzo-mixer with the CAPACITY for strong belting." I'm not looking for 100% belt-it-out-of-the-gate. Belting songs made for lighter mezzos with lots of mixing are ideal. Terezi is sarcastic, abrasive, boisterous, and witty, so character songs are great.

Some Options for song inspiration include
Catherine, Newsies--[Watch what Happens]
Millie, Thoroughly Modern Millie--[Gimme Gimme, Not For the Life of Me]
Sally OR Lucy, You're a Good Man Charlie Brown [Little known Facts. my New Philosophy]
Logainne, 25th Annual Putnam County Spelling Bee [Woe Is me] (note that I DON'T want a lisp for Terezi-but it's the right kind of voice placement.)

PS. Terezi also has the ability to be quite touchingly soft and intelligent, so adding a ballad to your audition would be a GREAT idea. Feel free to sing anything, as long as it's theatre!