I found a related post: https://japanese.stackexchange.com/a/73037/50132.
It seems like the conclusion was that it added a feeling of "当たり前".
According to the other post, (よ)うに can express regret, dissatisfaction, criticism, doubt, emotion, etc. What feeling does it add here?
ねえ お嬢ちゃん何か願い事はあるかしら。(めぐみん)願い事?。遠慮しないで言ってみて。(めぐみん)世界征服! ごっ ごめんね それは無理だわ。どういうことなのこの子 意外と大物なのかしら。えっと… ほかには何かなあい?(めぐみん)それじゃ 私を巨乳にしてください。ああ… それも無理かなあ。というか お嬢ちゃん 今いくつ?まだ そんな心配する年じゃないでしょうに。(めぐみん)なら… 私を魔王にしてください
Also audio: https://vocaroo.com/1oU3ur1dGKHk.
I wonder if this でしょうに also has a meaning like 当たり前 (something like "obviously that's not an age you worry about having 巨乳, (why would you even ask for it?)"). I assume it doesn't show any irritation about asking in this situation?
Or does this でしょうに maybe have something to do with age? めぐみん in this anime is a little child and the other woman is an adult.