I am sorry to hear that your puppy has firm stool hanging from her anus.
I would encourage you to get her to sit in a bath of warm water and epsom salts, that may soften the stool that is stuck and reduce painful swelling and inflammation, and allow her to pass the stool. Make sure to rinse her coat thoroughly after the bath to remove the salts.
If she is still eating and drinking normally and not vomiting there are a few other things we can do to help her.
One is to increase fiber by adding canned pumpkin (not pie filling, just pumpkin) to each meal. One teaspoon to each meal to start. This will make the stools softer and easier to pass.These are just guidelines, you can adjust the amount based on her ease passing stool as well as whether her stool is too soft.
Increasing the amount of fluids in her diet in general will help as well. You can add low salt chicken or beef broth to her food. The more fluids she takes in the better so if she likes to lick ice cubes give her those as well.
Slow walks can also sometimes help to get the intestinal tract moving properly.
If she begins vomiting or is no longer eating we are probably beyond home therapy. She needs to see a veterinarian. But you can use the above tips for preventative measures in the future. And if she seems to have chronic troubles with constipation pumpkin or higher fiber foods can be used chronically if needed.
I generally do not recommend laxatives or enemas in dogs. They don't tolerate them well, and we can see changes in blood electrolytes and severe dehydration result.
For long term gut health you might also wish to add a probiotic to get her gut bacteria back to normal. Fortiflora, Proviable or Benebac are very good ones.
Please let me know if you have any further questions.