Dog attacks in the dream stand for fake loyalty that turns around to harm you, while children represent innocence, new beginnings, blind trust, and lack of experience. Seeing a dog attack a child might represent an interaction between these qualities.
TL;DR: A dream about a dog attacking a child means that your trust in someone or something is misplaced and you will be harmed in the end.
Dream about a dog biting a child
To see a dog bite a child in the dream means that your trust in someone that pretends to be loyal may backfire and leave you disappointed, and this might make it hard for you to trust people in the future. You will no longer have the trusting attitude of a child and that is good, but it will also lead to trust issues.
Dream about a dog chasing a child
To see a dog chasing a child in the dream means that someone is trying to take advantage of you by acting as a loyal friend. They want to capitalize on your trust to get access to your world but it is not you they want. There is something you have that they are after.
Dream about a dog killing a child
Like I said earlier, a child in the dream might stand for new beginnings. Therefore, seeing a dog kill a child in the dream might mean that there is a new path you will take with a person you think is loyal to you. However, this person will only lead to the death of your goal right in its infancy.
Dream about a dog barking at a child
To see a dog barking at a child in the dream means that there are some people that you trust and that you think are loyal to you. However, these people give you their opinions and advice just to see stop you from advancing.
Like a barking dog, they say all sorts of things to bring you down, all the while acting like they care about you.