I was a similar kid to your daughter. Nothing my mother ever said could get me to wear a bra.
I did end up wearing one for a few years after a trusted camp counselor took me aside and talked to me- basically she just said if I ever wanted one, she'd be glad to get me one, no questions asked and threw in some other stuff about growing up. I thought about it for a few weeks and took her up on it eventually. And I still didn't say anything about it to my mother
That said, I've given them up again. The few years I did wear them I only wore sports bras. Now I wear undershirts (mens) or underarmour (also mens) if I need them to bounce less or am wearing something formal. I do have a large chest, and this works fine for me.
I would probably offer her some undershirts, and some underarmour. You might point out that even boys wear undershirts. Otherwise, I don't think its an issue. It makes you uncomfortable, but it obviously doesn't make her uncomfortable. I see one of two things happening- either she changes her mind as she matures, or peer pressure gets to her, or she'll decide she doesn't care about societal norms and continue as she is.