Ошибки есть. Сейчас укажу:
Next birthday I would like to have a puppy. I really want this present, because I love animals. I wants, that a puppy was small, with long white fure and short cute paws, dark eyes and nose, like a button. I will be very happy, if I get the puppy. I will play and walk with a puppy and take care. Me with will be best friends!
Конечно, в целом все правильно, но все же ошибки маленькие есть :)