I don't really understand the last line of this story...was

I don’t really understand the last line of this story…was it the author who is a ‘ugly girl’? Why?

Do you mean this line?
「ちなみに、ちょっと不細工な女の子です。」

No, I’m pretty sure that’s referring to the puppy.
[By the way, {the puppy} was a little plain looking girl {female dog}.]

Thank you!