It is my neighbor's dog that bit my child, and I don't want to "sue" them,do I really need to consult a lawyer?

You should always consult a lawyer before dealing with the insurance company.  I never contact your neighbor and harass or scare them.  I deal directly with their insurance company.  Often times, the quickest way to get past the difficulty of dealing with a bad situation with a neighbor is to turn it over to someone else to handle.  Remember, their insurance company is handling the situation for them and you would be wise to have an attorney handle it for you.