I have spent a good portion of scripture (especially in the Old Testament) relaying names, and so I hope to do that justice in this setting as well. This book of the Bible is extremely short, but extremely powerful, and I think there are quite a few reasons to deem it essential to scripture.
Firstly, it gives a story of redemption. That is the biblical theme, is it not? People whom we might deem unworthy of redemption are the people that God seems to focus on the most. The Israelites were certainly unworthy of God's attention, but they are focused on because they are the only ones in this entire planet willing to follow the Lord in seasons. No other nation would stay the course leading to the Messiah.
Secondly, (because Jonah is a prophet) we are given some useful prophecy in the New Testament life of Christ. Everything in the prophet's lives lead to Christ, whether you are reading from a major prophet of scripture or a minor prophet (minor because the book is short).
"For as Jonas was three days and three nights in the whale's belly; so shall the Son of man be three days and three nights in the heart of the earth." Matthew 12:40
Perhaps if Jesus had missed the opportunity to talk about Jonah, we would struggle with the legitimacy of this small book of the Bible. Thankfully Jesus speaks about it, and it lines up prophetically to Christ's death and resurrection. That is the key part of reading scripture. We must ask ourselves through every page "how does this line up with Christ's death and resurrection." You will find your answer every time (the Bible is great at that).
We are also given a small glimpse of Jonah in 2 Kings, and it's not a rough mention, but it's a mention nonetheless.
"He restored the coast of Israel from the entering of Hamath unto the sea of the plain, according to the word of the LORD God of Israel, which he spake by the hand of his servant Jonah, the son of Amittai, the prophet, which was of Gathhepher." 2 Kings 14:25
Thirdly (and lastly), this shows us a real struggle that Christians of all walks face. We can somewhat be harsh on the circumstance and leading of Jonah and think, "Boy this Jonah fellow is dramatic and not very bright." What we might miss, however, is that we fall into the same traps. We must be cautious about bragging on Jonah's lack of faith too much, because we are just as guilty of his mistakes.
That is really what we need to look at while we read, we must say, "Am I guilty of thinking this and being this way?" Of course Christ is the picture here, but it's a book that teaches us how to be more LIKE Christ rather than more like Jonah.