I'm looking to the GM for thoughts on which ship type Kaveri calls home (if she even does - that's an assumption from the Beginner's Set background for the character).
The Beginner's Set had her traveling with Hethan for a time, and then with Dao (another PC). So I think it wouldn't be a one-person ship like many starfighters. Perhaps a small freighter? Could be that, as a Hunter, she has had to acquire quarry sometimes (rather than just killing), and that would require transport. I haven't played this game much, and ships have never come into play so far when I have, so I'm a bit at sea with this. A G9 rigger, perhaps? I could see that a Pathfinder scout ship might make sense, too, though it would mean that not everyone could travel together in one ship.