Many times a child will develop his/her game and playing skills way before they develop their social skills. A typical example is where a tennis prodigy out performs all of his/her local competition of the same age. At this point, many parents feel compelled to advance the child by having the child play with older children. Sometimes this works, but usually the prodigy feels awkward and out of place and may have trouble maintaining friendships. You can remember how embarrassing and awkward it was when younger players beat you. Remember how your peers teased you about it.
In actuality, most young players will not develop into a world class player. In order to allow your child to develop socially, try to encourage them to play with children their own age as long as possible. By the age of 15 most kids will have developed most of their social skills to the point where they are able to deal more confidently with older children.
Just because you think your child is a great tennis player now, it does not assure success later. Allow your child to develop a love of the game for a lifetime. Allow them to develop his/her social skills. These skills will help them for the rest of their lives. In my experience, I see more kids being "burned-out" by parents pushing too soon. I know it is difficult for parents to be objective when their child is so enthusiastic about playing and progressing quickly in their playing skills. However, the parent is the only one that can help them find a balance in their training and playing commitments and in their social activities in other diverse situations. Find a way for your child to be involved in other activities and maintain friendships with children not associated with tennis. This will help assure a balance in their lives and possibly result in less of a danger for over saturation and ultimately "burn-out."
Good luck on the court!