Whippets are not nearly as delicate as they appear and are usually excellent with gentle children. As long as a child is old enough to know how to treat him and is taught how to play with dogs, a whippet is a good choice for a child. A very young child should never be left alone with a dog of any breed and interaction between a child and a puppy must be closely supervised, for the protection of both.
For some excellent information about kids and dogs, see Diamonds in the Ruff: Toddlers and Dogs. If you have older children, they'll enjoy the activity-intensive How to Love Your Dog.