A dog can be a kid's best friend. Kids tend to love dogs! And if your family has a dog, it probably won't be long before your child is asking to take the dog out alone, without adult supervision.
Think carefully about your answer on this. It's going to depend on several factors, including your child's skills, the dog's skills, and the environment. Here are some things to consider:
Size of child and size of dog. In general, a dog that's 30% or less of the handler's body weight is going to be relatively easy to control. A dog that's 50% or more is going to be difficult or impossible to control without specialized training or equipment.
Is the child the only one who's walking the dog day to day? Kids often lack the ability to do consistent leash-walking. The dog frequently ends up pulling. Over time, this will cause the dog to lose much of his loose-leash skills, and begin to pull more and more. It's a good idea for an adult to walk the dog at least a couple of times during the week to review leash skills. Of course you'll also be coaching your child on how to prevent pulling and how to respond if the dog pulls, but this is a long-term learning project for most kids!
How's your child's ability to focus? While on a walk, whoever's got the leash is who's responsible for the dog. If your child has a tendency to get distracted and forget about the dog, it might be a good idea to accompany them on walks for a while to remind the child to focus, or to take the dog when the child needs a break.
What's your dog's temperament like? Is it an easy-going dog who's unflappable around many situations? This type of dog will be easier and safer for a child than a dog who's nervous. A dog who's reactive toward people or other dogs is never a good choice for a child to walk alone.
What would your child do in a worst-case scenario? This would usually be something like the dog is pulling after a cat or squirrel and the child has lost control and is being dragged, or an off-leash dog approaches your dog and there is a fight. What is the child supposed to do in this kind of situation? There's no one-size-fits-all answer for this; it will depend on many environmental factors, so the child needs to have the ability to make quick decisions on his or her own. This is an advanced level of cognitive functioning, so younger kids may not be able to do it at all, and older kids might not make the best choices. You can talk through some potential situations and see what your child thinks; above all the child should be conscious of his or her personal safety (including dropping the leash if needed to get away from a dangerous loose dog), and also think of the dog and of other people and dogs in the environment. It's most convenient to instruct the child to simply avoid potential conflicts, turning around or moving away when he sees one, but that's not always possible.
If you do not live in an environment that you consider safe for your child to walk the dog alone, try to think of some options that will still let your child and dog have fun and safe time together. Maybe you could take them on a hike and let them lead the way while you trail behind. Maybe you can let them walk on a path in a park while you read on a bench. Maybe they can walk the dog in the company of friends or siblings; if anything goes wrong at least they'll have some extra hands to help. Make your decisions about kids and dogs carefully, and I hope they have a lot of fun together and stay very safe!