Happier? Not necessarily. Remember, you're thinking about this from an adult perspective. He's still a child, no matter how bright he is at this point.
I've been teaching for 11 years. I have a bachelors in special education, a masters in administration, and am a national board certified teacher. I've run the gamut in so far as teaching; I've taught severe special ed. students (wheelchair bound, mentally challenged), to mild (autistic, apergers syndrome (form of autistm), learning disabled students, etc.), to inclusion classes, to honors, to AP Literature and Composition. I don't know that I would consider myself an expert, but I've worked with many types of students and feel that I can give you some sound advice.
First, you should consult his pediatrician and have him tested by an expert. There is a vast difference between being gifted and being autistic. If he is autistic, then he may display some or all of these characteristics: have little eye contact, difficulty with social relationships with everyone, lack make-believe or play skills, difficulty communicating verbally (starting sentences, etc.), an attachment to an object, little interest in experiences, etc. If you son displays some or all of these characteristics, he may be autistic. Again, have him tested.
Regardless of the outcome of testing, his intelligence may very well be creating a lack of interest in school. In short, he may be bored, even though he skipped a whole grade. Find his interests and go with it. I once had a very bright young man. I taught him when he was in 10th grade. His mother told me when he was 3 years old, he showed an interest in medicine. At 3 years of age, he asked her where babies came from. She took him to the library, showed him how to find books, and explained the process to him. That was 11 years ago. He is a successful doctor. Whatever his interest(s), give him more; challenge him to think and to do, whether this means building something, cooking, etc. Just because he skipped a grade doesn't automatically mean that all of his needs are being met. You need to extend his learning as a parent. Remember, we invest in that which we value. In this case, it would be your child's education.
In regards to him not wanting to do his homework because it is boring or too hard (when you know it isn't), this is the time when revoking privileges works wonders. Actions speak louder than words. By revoking privileges, he'll see that doing homework is important to you. He'll see what you value. It may be hard at first, but as he gets older, he'll take those work/study habits that you help him create today and carry them with him all of his life.
Well, I hope this helps. Let me know how it goes.
Sincerely,
M.