how about " she sets a date?"
Could 'she fixes a date' be okay?
or "she sets a date"?
"She sets a date" and "She fixes a date" are both more natural than "She establishes a date". (I am a native speaker from the US)
I'm not so concerned about what is natural in English since I already speak that fluently; I'd be more interested in knowing if this is the more natural way of saying it in Spanish.
It is probably not related but it reminds me I once said, "I'm fixen to"(Texan) and one of my college professors thought it was hilarious.