Dog is carnivores, it eats many kinds of animals, if given to it,
but generally, it kills & does not eat. Vomition is an act of getting out the frog from stomach, it is good thing, I have not encountered such situations as like you, in my opinion, it may digest the frog, by its digestive juices, or more prompt, the frog should be removed by laparotomy means by surgical operation, it is done well. Frogs have obnoxious glands on its skin, due to which there will be vomiting,