I have the same problem with having to transpose songs into a lower register and learn all mine by ear as I don't read music.

I agree with the above advice - sing what you feel comfortable with and in the way you prefer. There is so much good folk music out there, if your teacher's knowledge is small then you can help her expand that knowledge by doing something she doesn't know.

Singing should be a pleasurable thing - if you're not getting paid for it why sing something that you don't like or that doesn't suit you?