No. She doesn't even know there is a dragon.
But didn't she mention it in the beginning saying that it was going to destroy the world because it was dumped that's why she went to get the beastmen
No. It was the son of the demon king. The original story had the son picked up as a kitten from the market and given to Clarence (golden retriever girl) and she then kicked him out because she did not want him. That filled him with hatred and caused him to grow stronger then eventually become the demon lord trying to destroy the world. (BTW, the son is the other little one actin picked up with the black body and white paws, the little boy.)
So I dragon came out of nowhere
Does the FL know who the dragon is?