My son just started playing in the 10s when he was 10(last April), after having about 9 months of privates and group clinics. He lost right out of the gate but after 2 tournaments he came out winning and even won 1st place in a level 6 tournament. He's been playing tournaments now for 13 months and has moved into the 12s and is currently ranked in the top 20. He's only ranked this high, though, because he's hooked on playing tournaments and they've become his social scene, LOL!
On the other hand, he has a friend who started playing tournaments at the same time as him(they're almost exactly the same age, too) and this boy has maybe one won match in a USTA tournament in a whole year. His mother even pulled him out of tournaments back in February, but he tried again last month and lost both his rounds. Yet, he's a determined boy and LOVES tennis so he just keeps plugging along.
Like TennisCoach in FL says, only you know your child. What can they emotionally handle? How committed are they to improving or are they just playing to win? How committed are YOU to the cost and travel of tournaments?
My son has grown a LOT by getting out and playing matches against friends. He plays girls that he is evenly matched against and boys, when we can find them and get together with them all! The most important thing is that they get match play and lots of it. So, I'd suggest getting phone numbers of other kids and start talking to parents and set up some play time. Tell them you'll bring the Gatorade if they bring the food bars, LOL!
My son will even fill in with the men's doubles leagues if they need a 4th player! He'll hit with you if you're 80 or if you're 8. If you want to get on a court, he'll be there with you! That's just what the passion of tennis does to him. He loves the sport, but moreover, he is a happy kid on court. He is pleasant to the other kids and he has a great attitude about winning or losing. Ok, sorry for the book here! Just keep those lines of communication open and make sure you're checking in regularly with your kid to make sure you guys are on the same page as a family. It will all fall into place as you go along. Good luck!