"She is going to the pool to swim."
Translation:Вона іде у басейн, щоб плавати.
Yes, definitely correct at least on a spoken level :) I would say it like this. But actually don't know whether it's a bookish way as well.
At the same time though, we can't start questions with 'чи' because that is too bookish...
Firstly, this is a statement here. Secondly, if it was a question, with чи it sounds more like contemplating, thinking aloud: "Гммм, а чи йде вона сьогодні плавати?", not as a direct question to a person, unless you do "Не знаєш, чи вона сьогодні йде плавати?", in this case it's just same as "whether"
Also quite spoken, if it's a question of the type "Would you like...": Чи не хочеш ти сьогодні піти в басейн?
Otherwise it's not bookish, but poetic: [sigh] Чи йде вона сьогодні плавати?...
but still sounds like contemplating aloud during a dramatic poetic monologue :D