Hi! This is a bit tricky, but I'm sure somebody will know:
Can you say: "Her nature of being nasty didn't impress me" or "her character of being cruel wasn't welcomed at the school"?
You can say them, and you're likely to be understood; but I'm not sure they're altogether idiomatic. So they may sound a little odd to many native speakers.
In the phrases "nature of X" and "character of Y", it's more usual for X and Y to be the person or thing whose nature or character it is.
In your sentences, however, X and Y refer to the qualities themselves.
Why not use the more customary forms: "her nasty nature" and "her cruel character"?
All the best,