Well, technically, and it's probably not what you're looking for, but Yams/sweet potatoes/potatoes are considerd as root vegetables....
tHERE IS PEAS, LETTUCE, BEETS, CAULIFLOWER, pumpkin, green peppers,...hell, I don't know what she likes. Go to the grocery store and find stuff.
Also, is she on a Keto type diet because you mentioned..."There aren't too many carbs in tomatoes and carrots?" Can you elaborate on this a bit, and also, why can't she eat broccoli, etc...?
More info please.
BMJ