This is such a difficult question and solely depends on the individual and their concentration span and their work ethic. I have known 6 year olds practise like they are 26 and I have known 12 year olds not have high enough concentration levels. It is down to the individual.
I am a big believer though that getting youngsters into a martial art at an extremely young age is not always a good thing. You find that the earlier they start the quicker they get bored. In my experience 8-12 years old is the perfect age, as they are there because they want to be and can hopefully grasp concepts a lot quicker and progress faster.
That said check out 7 year old Ruby who has been practising for 9 months. If she continues at this rate she will be a force to be reckoned with. My advice is to wait until the child is keen and wants to go themselves and see how they get on. The Instructor will be able to tell you after the first few lessons if it's best to leave training for a while or whether they can cope.