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“Once upon a time, there was a little cat named Little Meow, living on a little farm. Life on the farm was gloomy, so Little decided to leave the farm for a new beginning. That morning, while everyone was busy working, she snuck away without looking back. Towards evening, Little went to a small bakery for a lie-down because of growing tired. With a lovely appearance and big brown eyes, she was adopted by the owners. She played with and was always by their little daughter's side, Anna. One day, Little accidentally was seriously injured in her leg, which she did not live much longer. Anna, therefore, was so heartbroken. On a dull snowy day, Little eventually was gone. Anna could not come back home in time to see her for the last time. Due to so much grief, she was crying all night long. Years later, Anna grew up and met more friends. However, Little was the best and most special friend staying forever in her heart ”

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You should use the cat's full name throughout. Changing only that and what is not good English:

“Once upon a time, there was a little cat named Little Meow, living on a little farm. Life on the farm was gloomy, so Little Meow decided to leave the farm for a new beginning. That morning, while everyone was busy working, she snuck away without looking back. Towards evening, Little Meow went to a small bakery for a lie-down because she was tired. With her lovely appearance and big brown eyes, she was adopted by the owners. She played with their little daughter, Anna, and was always by her side. One day, Little Meow's leg was seriously injured in an accident, and she did not live much longer. On a dull snowy day, Little Meow eventually died. Anna was so heartbroken. Anna could not get back home in time to see her for the last time. From so much grief, she cried all night long. As the years went by, Anna grew up and met more friends, but Little Meow was always her best and most special friend, staying forever in her heart.