OK, I want to take one more crack at this, this time without tongue in cheek. As a parent, I find that I always want my kids to excel. But, as a parent, I have a bigger responsibility to make the executive decision as to what is best for my children. When a child shows a special gift in an area, my belief is to get the best possible resources available to help that child realize their gift whatever it might be. To that end, there is also the possibility that a child might be pushed to far to fast.
This is where it gets tough as it can be very hard to discern what is to far and to fast. It can also be impossible to know what problems might arise in the future due to a decision that you might make now. As an adolescent, building self confidence through accomplishment is a great benefit, and the sport of gymnastics goes a long way to this end. It builds physical strength through conditioning. It builds coordination through repeated physical movement. It builds character, discipline and lasting relationships through the spirit of team competition.
Even as a member of a team, you must compete as an individual. While the joy of winning is always your first goal, you must also route for your team members and show good sportsmanship in success and failure - while you might win, your team might lose and when you might lose, the group as a whole might win - You will learn to face your fears and conquer them. This is a great life lesson as you will learn that the only failure is not trying.
These are the things that we should strive for our children to get out of gymnastics. While it might be easy to get caught up in the hype of pushing a young child to leave her peers behind to compete with the older athletes, much will be lost as well. The age of six just seems so young to be pushed ahead by an eager coach. It's easy to let these coaches get in your head as they are likely telling you how amazing your child is...something as parents we already know, but like to hear anyway.
I would love to see you take a deep breath and step away from the situation for a moment and seriously consider the possibility that it's too soon. If she's that talented, a year won't make a difference. Maybe there are examples of kids who traveled this route and went on to be very successful, but it is helpful to step back and consider at what cost. You're only young once. Some kids will sacrifice much just to please their parents but ultimately it is our responsibility to make the executive decision as to what is best for their well being.