This may be a sticky situation to involve yourself in. Since I do not know the girl I am not sure to as her feelings towards you and this dating. She may take your kindness as romantic interest no matter what you tell her.
What you are suggestiuon is extremely nice, and gentlemanly but make sure you make it 100% clear it is not romantic before you take her out, and judge her reaction to you asking her, mostly be careful not to enage her feelings by accident. Good luck!