I feel like this doesn't sound like something a native English speaker would ever say... but i'm not sure how to translate it then to something more normal sounding... Perhaps in the UK or Commonwealth countries this sounds more normal than in the US?
It really doesn't (in the UK) - I originally answered 'She has done higher education' because that at least made some kind of sense, even if it wasn't very elegant! But HE is not something you have.
I can only think of 'She has been through higher education', but to be honest I would usually just say 'been to university' or 'has a degree'.
Is this in the sense of "she has gone to university" or "she has more education than someone else", either, or neither?
In the sense of "she has gone to the university" or any other institutions of tertiary education.