I would certainly report the incident. The speeding was bad enough. It is a shame, but they will most likely not do anything at all about your dog getting hit. Still, the speeding should be reported. Also, since you know the person, here is what I would do:
I would go and get a little "Thank You" note card and write ont he inside:
"After you ran over my dog and left him limping and bleeding, as (child's name) and I watched in horror, we rushed him to the vet. His leg was not broken and he is going to be ok, thank goodness. It would have been so very hard to lose him since he is a member of our family.
We thought you would certainly want to know that he is going to be fine after all the concern that you have shown. Thank you so much for that. The way one treats an animal tells the world all about them."
I know. It may be very sarcastic, but that is how I would handle it. The police are really not going to do anything, even about the speeding issue, but I would probably file a report anyway. Even if nothing comes of it, should this idiot be speeding along and hit a child, at least there will be an incident report on file documenting his carelessness. I would also send the note as that would give me the satisfaction of knowing that HE KNOWS I saw what he did.
I am very glad your dog is going to be ok. That must have been very traumatic for both you and your child. I am like you. If I hit an animal, especially someones pet, I would have to stop and see if there was anything at all I could do. I would feel terrible about it; it would have been an accident, but I would not compound the hurt by driving away.