This is a very common query from local parents and friends. I think eight or nine years old is about the youngest age when children are likely to have the finger strength, concentration and ability to stay still long enough to practise and get the most out of lessons.
I've had phone calls from parents of children as young as four years asking this question. I've advised them to wait before they pursue the guitar idea and instead focus on their child learning about music, perhaps with percussion and keyboard instruments. More important than anything though is listening to lots of music - just have the radio on! That's what hooked me many years ago.
If your child is younger than eleven you will probably need to buy them a smaller guitar, where the scale length of the neck and the body are shorter than the usual. Then as they get older they will need a full size and full length guitar. There is more choice in acoustic guitars than there has even been and I can offer advice on the options out there. It's important to get the right body size even in a full size guitar - this can be more important that length sometimes. Some guitar bodies can be too large for some smaller people (adults as well as children).
From the age of about eleven or twelve and into the early teen years is often the peak time for learning and advancing for many children who play the guitar, due to increased maturity, finger strength and concentration. That's the time when kids who are really into it can explore and discover the music that means the most to them. This is applies to musicians and music fans alike - and great musicians are the biggest music fans there are.
Of course, you can start to play the guitar at any age (I have students who started aged 70 or over) and can make good progress if you have the commitment and love of music.