I think to explain that away and the requirement to hold her breath, how about her power envelops her in a sort of dimensional shield that covers her skin, hair, eyes, nose, etc. So she keeps the air already in her lungs when she shifts into this other dimension, and possibly anything else that she extends the shield onto, like her clothes, or a bag, or another person...

Of course, this shield is just there to keep her together in this other dimension: different dimension means different physics, which means her molecules are going to behave differently. Which could easily mean she will quickly turn to soup. It doesn't do anything else. Not that I can think of anyway..