As long as the dog is "well mannered" then I think it is okay to get an older dog if you really want one. For safety, don't leave your child alone with the dog even if you and the dog get to know each other really well already. A puppy seems safe because they are smaller but puppies are innocent and they need to be taught and trained. They might end up playfully hurting your child too. There are many dogs in shelters and you might find a perfect dog there. Read up on dogs first in order to learn about the personalities of each breed. Choose a breed or a half bred mutt that are great and friendly with children. Also make sure that the shots of the dog are complete. I hope you consider a shelter so you can save a dog's life.
