No, God doesn't want you to be unhappy, but this doesn't necessarily mean that you ought to quit your job, or that this would be God's solution to your unhappiness. After all, wouldn't you be even more unhappy if you found yourself unemployed for an extended period of time?
You see, when we find ourselves unsettled or unhappy it doesn't necessarily mean that God wants to change our situation. Sometimes He does, but not always -- and it's important to understand this. Instead of changing our situation, He may want to change us -- to give us the patience and the inner strength we need to stay with it. In other words, escaping from something we don't like isn't always God's will.
I often think of the Apostle Paul in this connection. Several times he found himself thrown into prison because of his refusal to stop preaching the Gospel. I have no doubt that if he'd had a choice, he would have wanted to be free. Instead, he turned to God and found the inner strength he needed to overcome his discouragement. In the midst of prison, he declared, "I can do everything through him who gives me strength" (Philippians 4:13).
Open your heart and life to Jesus Christ, and then seek His will about your future. Then make it your goal to be faithful in your responsibilities, and to ask Him every day for His strength and contentment wherever He puts you.