"...про нову хату." should also be accepted. It is correct & many use the word "хата" (house) more often than "будинок" (which literally means 'building' and can get confusing.)
It's a possible translation, but "She dreamt about a new house" is much more common.
"The new house" would usually refer to a real house (unless it refers to some recurring fantasy).
«Мріяла про» usually refers to fantasies, not to real things. So, we're less likely to use «мріяти про новий будинок» about some specific house because that new house is not a fantasy, it's reality. It's not 100% required, but "She dreamt about a new house" would be a much more common translation.