Hi Ian
There's thousands and thousands of dogs in this country, owned by responsible people and non responsible people.
Hopefully this won't happen to another child, but a friend of mine's six year old boy was terrified of dogs, I'd go so far as to say he had a morbid fear of them.
His dad took him on the park, a spaniel off lead went bounding towards the boy. The boy was on a mini moto with a fixed speed of five miles per hour, wearing all the safety gear. He panicked when he saw the dog coming towards him and drove off and crashed into a concrete post. He died there and then.
Now, personally, I wouldn't put a six year old child on a mini moto, speed restricted or not and maybe it wasn't such a good idea to take the child on a park where it's obvious some dogs will be off lead (particulary when we had a six acre field he could ride it in). So so very sad.
If your daughter doesn't want anything to do with dogs, let her be but don't make a massive issue of it. Some dogs are friendly, some arn't same as some dogs won't jump up but some will.
Hope you get it sorted.
Lisa