G.♣.
I really don't think her breathing is related. If she's talking and needs to take a breath, she will. She might not be aware of it, but she will breath if she needs to.
There could be many reasons why she sounds nasally when she speaks. Why not just give your pediatrician's office a call and see what they have to say about it. Maybe there is a medical issue that could be resolved. It could also be a case of her not using her muscles properly. I agree that a speech therapist does so much more than simply teach articulation. It's very possible a speech therapist could be helpful here.
Rather than speculate on what could cause it, I would just call the ped's office. They really are your first goto to try and figure this out.