Hannah is Barley and May's dog.
This is the way for your dog and Hannah to have puppies:

Go to Barley everyday and give him either miso soup or buckwheat noodles.
Hold your dog and talk to Hannah.
Then give Barley the soup or noodles.
Hold the dog and talk to Barley.
Hold the dog and talk to May.
At 1 pm May will be at the church.
Talk to her with your dog again.

Do this for aa while and eventually you will have puppies!