At first, I felt it as "I'm breathing on behalf of you". Then I said "OK, it's like There is a point/a purpose in my breathing, and this purpose is you, being with you".
Now that I've reached the end, and I see that you wrote it for your daughter, well,... I keep both of the above, because as parents sometimes we feel we are breathing on behalf of our children.
This has its cute side, but it's also dangerous, if we don't know how to manage it in our minds.
We need to remind ourselves (and pass the message on to our children) that they are perfectly capable of breathing (and "breathing") without us.
Again: we have to be really free to let others(including our children) be free, too.
(I know that you agree)
This poem is so authentic, Jack.
And like all of your poems, it is as if noesis, your mind, and your brain moved your heart to write it.