The unofficial 10 and under world championships is a tournament in Pula, Croatia, called Smirkva Bowl. Of course, this is a matter of opinion and others may say some different tournament is the best - like the Orange Bowl vs. Tarbes debate.
This year's edition will start next week.
The winner last year, as Monica_Rules says, was Eleanor Dean from Britain. Dean actually beat her opponent in the finals by 6-0 6-0.
Draw from last year - http://www.smrikve.com/smrikva-bowl/file_download/6
[Note that the drawsheet says that she is Spanish, which is probably (as far as I know!) a mistake. She trains in Marbella, which may have led to this confusion.]
But let's not get too excited. Players who dominate tennis early on often end up being unsuccessful in the pros.
My opinion doesn't count for much as I don't exactly spend my free time watching 10 year olds play, but it's probably because - a) It's dominated by girls who physically mature early on. Of course, the advantage wears off with time. b) It's dominated by early starters. Obviously, a girl who started playing tennis at the age of 3 would have a massive advantage over someone who started at the age of 7. c) Many top players do not compete outside their country when they are 9 or 10.
It's probably too early to say whether Dean will do anything big or not. But she is surely going in the right direction, so good luck to her.