The problem with your translation is primarily the word "the", implying a specific group of girls. The Hungarian sentence just means that there aren't any beautiful girls here in general (either). I believe if you omitted "the", your translation would be correct... but still kind of unnatural-sounding. (Duo's translation is the best, I believe)
"There are no ...., either" is correct here.
Here, we are talking about this place, and whether there are beautiful girls here.
In your sentence, "The beautiful girls are not here, either", you are talking about the girls and whether they are here.
Those are two different statements (két különböző állítás).