Strictly stating, this is impossible, because a whale is a mammal and not a fish. To the people of Jonah s day all creatures living in the water were fish. Man did not start categorizing living things until thousands of years later. The importance is not that God was in charge of Jonah s life and that His will would be done. We must not let our scientific knowledge spoil the meaning of the story.
Lets look at the creation of the world.
Suppose the first chapter of the Bible was written in the technical terms of the people of today. He could have said that creation of the earth took 163 million years. God created the earth that is the main point. How He did it is immaterial. Personally I do have problems accepting the fact that I evolved from a lower life form.