There are other similar expressions, though, and just because this one seems to make some kinda sense doesn’t mean it’s original, or unrelated to the others. It seems to be a general expression of surprise – so what’s thet got to do with being a newborn? I have an example from the mid-1960s that’s always amazed and amused me:
“Well pour me out and call me buttermilk”
I’ve never seen it before or since, but it’s clearly built along the same lines as the other examples.