What Can You Feed A One Month Old Puppy If Momma Dog Won't Nurse Pups Very Much Since She Is Getting Cut Up And Scratched Too Often?

You can start the gradual weaning process now. Her starting to get annoyed is how they learn what no means and a natural part of the behavior forming process. As you feed and are able to thicken the consistency they nurse less and less. Shallow bowl, putting some newspaper down under is a good idea since it's messy at first and some watered down canned or with a some pieces of soaked dry to start and gradually change it and add to it until they are eating normally. You can add a little puppy replacement formula and it may help if they are a little hesitant at first. Start offering around twice or even three times a day and as they do better more often and up the consistency. They'll be trying to eat out of her bowls in no time. As a food suggestion has been made, I feed Innova, green bag and would not ever feed my dog's something like purina or kibbles and bits or anything personally. You can check out food and reviews on the analysis site and the second link is a run down on how to actually read a bag of dog food if your interested.
They need to be at least 8 weeks (breed matters, some are longer and most of the time it's much longer) before they go anywhere though, and actually the law in many states, and have been started on their shots and dewormings and a vet check. It isn't about when they can eat, it's about health and setting the foundation for proper socialization and behavior in the future through interactions coming up (bite inhibition usually doesn't even start until around 7 or 8 weeks) If you haven't yet you should speak to your vet and get the appropriate dosages and dewormer (no OTC) from your vet for Dam and pups and start that now. You can probably just drop by and pick it up and they can advise you when you should start vaccines. Good Luck.
www.dogfoodanalysis.com  
www.bornfreeusa.org
www.terrificpets.com