Actually, according to Numbers 26:65 in Biblical days dogs were people.
ולא נותר מהם איש כי אם כלב
There was no man left from them except for a dog.
Therefore, Jonah must have been swallowed by a person. We know that it is possible for a person to swallow another person based on two Talmudic passages. In Keritot 14a we find that a person's throat can hold two olives:
ושיערו חכמים דאין בית הבליעה מחזיק יותר משני זיתים
And the Sages assessed that the throat can hold no more than two olives.
In Bava Metziah 21b we see that olives are people:
אמר רבי אבהו שאני זית הואיל וחזותו מוכיח עליו ואע"ג דנתרין זיתי מידע ידיע דוכתא דאיניש איניש הוא
R. Abahu said: "The olive is different since its appearance proves it; and even though the olive falls, its place is surely known because a man it is a man."
Thus, a human throat can hold two people. Therefore the dog – being a person – would have been able to swallow Jonah (who was only one person) with plenty of room to spare.