You have received alot of information on this thread. Most of it good....
At 10 weeks of age, the pup was doing exactly what it would do if it was still with the rest of the litter. It was normal behavior. What would have happened in the "pack" is that the other pup would have either backed off or would have bit the other pup back. Obviously your little daughter is too young to exert any dominance (alpha) behavior. So from now on, the daughter must be kept away from the pup when it has a food object. Adult humans need to mess with the pup when it has a food object, and if the pup is aggressive/protective at that time, the human adult should make the proper correction.
It wasn't the 10 week old pup's fault. It was just being a 10 week old pup. It needs to "learn it's place", but a one year old human isn't capable of doing so.
You need to establish dominance with the dog. You don't need to be physical. While all three of our dogs I roll them over and let my son stand over them while they are on their back. A dog on it's back is the most submissive stance for a dog. With your daughter standing over it the dog realizes that she is more dominant than her. Just my 2 cents.
Basically, I bit him back. I would grab him by the scruff of the neck and growl at him and even shake some. I had to be a little rough. I also would spray a mixture of 3 parts water to one part vinegar at his nose (not his eyes). Now he's one of the nicest dogs I know. A great dog and quite trustworthy. Bite your dog back now and you won't have to later.
I agree with the above quotes for the most part... I have had Wolves, Wolf/hybrids for years and now have an Argentine Dogo. I have actually never had a problem with any of my animals, all are trained to hand signals and have been/are exceptional animals. Sadly in the past 30 yrs some have been lost to old age.
I agree that there is no need to be physical with the exception of the very first instance of a growl, or nip/bite when a pup. Tried and true method for me has been rather than just roll them over to present their belly,,, You need to grip their neck(under their throat) as if it was their mom biting them and shake...(hard enough for them to know it!! and growl too, as if their mom was giving them the bite ( pinching hard enough on their neck skin that they know it....not to damage them for life) Then without saying anything immediately put them on their back belly up, the most submissive posture they can have. Have your daughter stand over them if you want but usually once you establish the "Alpha" in the group (which should be you) all should progress from there hopefully. My advise other than what has been said would be teach with love, dicipline, and use tonal inflection not physical punishment for training. The only thing I have ever had to use was the above method to reinforce dominance and that I was the Alpha.
I have had very large dogs for years and all have been well trained, wonderful companions and family members. However, I did make my mother a promise when I got my first wolf/hybrid 30 yrs ago that he would be well trained. He was.....and all have been since. Where I draw the bottom line is that once they are past their puppy hood and trained, if there is a bite due to agression of any type, to either me, or my son. The animal will be dog gone. That may sound harsh but....if they show that type of agression and are past the pup stage...it is a red flag and a sign of future problems. JMHO. Good luck and keep us posted.
P.S. I should also have stated that I have all of my animals spayed or neutered(sp) as soon as they were old enough to avoid their natural dominance behavior such as Testosterone in males( It makes a huge difference). But then I had no plan on breeding. No offence to any one....
Again, Good Luck!!!