Walmart used to allow small dogs into their stores and even emotional support dogs.
But Walmart no longer allows any dogs into their stores even small dogs or emotional support dogs.
However Walmart Still allows dogs into their stores if they are an actual service dog that has gone through training to assist the person who needs the dog.
But emotional support dogs are no longer allowed because they're not recognized as a needed legal support animal like the service dogs are.
So no you won't be able to take the small dog into the Walmart Store even if you carry it in a bag.