Don't you wish someone had given you a crystal ball when you became a mom so you could see the future? It's so hard to make some of these decisions!
I have four kids, at least 3 of whom are gifted. They are VERY different. What has worked for one has been disastrous for another, so my best advice is to really trust yourself as a mom that you know your child best. Use that to make your decision. It sounds like you already know that if your child doesn't learn to move through challenges and develop problem-solving skills now, it will only be more frustrating and damaging to his self-esteem later.
We decided to move our second child ahead after first grade. I wish we had done it sooner. We used an evaluation process called the Iowa Acceleration Scale, which was fantastic. It uses a lot of different information, including IQ tests, academic performance tests, teacher input, family interviews, etc. to help make a decision about acceleration. It can help families and schools decide what level of acceleration is appropriate for the child (grade level, subject level, etc.) It really helped us because it took some of the stress off of us as parents. We weren't just saying, "Hey, we think our kid is really smart." The total evaluation was saying, "Hey, this kid is able to function way beyond his grade peers and needs intervention. These are the things that would be appropriate." The IAS also provides planning for follow-up to see if the decisions that were made are working.
Our son is now in fourth grade and he's doing pretty well. He is still above grade level in a lot of areas, but is more challenged than he was. He's made friends and our G/T teacher is working with him on social issues. He does sports and, while he isn't the best on his team, he is also not the worst. Overall, acceleration has been a good decision for our son.
Best of luck to you!