DON'T PUT YOUR DOG TO SLEEP DO NOT! Teach your daughter to respect a dog and now she knows that is what will happen when she annoys a dog when they are sleeping. I was bitten by a dog 3 different times when I was 4, 6, and 12, the dog was only put to sleep after she was 16 years old and about to die anyways, I still bear the scars but you know its okay, it was a learning lesson and I never bothered a dog again.
I understand the need to protect your child, I'm the same with my son and my dog, but you also have to realize that the dogs will be dogs, and that your daughter invaded her space and surprised the dog and the dog did the natrual response with believing she was being attacked. Your child needs to learn to respect an animals space and understand that doing things like that are not nice, its just like with pulling on tails or ears, its not nice.
Bottom line is don't put your dog to sleep, its not fair to the dog. You need to teach your daughter to respect animals space. Also it wouldn't be fair to your husband or yourself if you put your companion down. The dog did what dogs do, don't punish her for that, just teach your child to respect the space and the animals.