The short answer: No.
The long answer: Just like cow milk, goat milk can do more harm to your cat than good. The reason behind it is that adult cats cannot process the carbohydrate found in goat milk due to the lack of lactase in their digestive system. Even young kittens that produce lactase in their stomachs will not be able to handle the high amount of lactose found in goat milk. Aside from that, goat milk does not have the right levels of protein and fat needed by cats.
A cat who drinks goat milk will most likely get an upset stomach. Symptoms include vomiting, bloating, diarrhea, and intestinal cramps. If you feed your cat goat milk for prolonged periods and beyond the recommended amount (5 to 10% of her daily caloric intake), it may also cause her to gain weight and become obese.
What to do if your cat accidentally drinks goat milk: Observe any changes in your cat in the next 24 hours. If her symptoms worsen, take her to the veterinarian immediately.
In summary: A type of milk derived from goats, goat milk is not recommended for young kittens and full-grown cats because it does not contain the proper calories and nutrients they need. Kittens should only be fed goat milk in dire circumstances, never as a permanent meal plan. But before doing so, you should get your veterinarian’s approval.