I was actually thinking about the same thing and decided it was entirely possible all the therapists had been killed. We don't know what the population of the colonies was pre-attack, but it at least seems like a hell of a bottleneck--they may well have lost entire categories of people just by chance.
Anyway, she'd need years and years of therapy and it would be incredibly boring. It's one of those "if they were real and I wished them well, they should do X; because they're fictional and exist to entertain me, far better that they not do X" things.
Yeah, it's entirely possible there wouldn't be any therapists left. But I think that even if there were one, or even just someone who was good at talking to people, they'd be snaffled by Galactica to keep the pilots on an even(ish) keel.
But yeah, it wouldn't exactly make for good TV! Unless the therapist turned out to be a cylon, or to have some other kind of weird agenda, but they already kinda did that with Brother Whatshisname and the Chief, so that would be boring.
I think Kara is a fascinating character, and a lot of that is her broken-ness. But ye gods sometimes it's traumatic, watching her hurt herself and other people. Ouchypants.