Are the kibble pieces pretty much whole when she vomits? Does it happen soon after she eats? She could be scarf-n-barfin. Try feeding her canned food instead, which is much better for cats anyway. Some good brands are Wellness, Nature's Variety, By Nature, Weruva, Precise, Go!, etc. www.catinfo.org
Is there somewhere you can put the dog's food where she can't get it? It's not a good idea for cats to eat very much dog food, especially a growing kitten. Doesn't have the right nutrients.