Null just posted an responder showing Padmé just after giving birth:
To my untrained eye, it looks too constraining to be able to give birth while under that cover. Does it expand? Was it only placed over her after giving birth?
Is there a canon explanation for how this works? Perhaps the droid delivered the baby and then immediately placed the cover over her.
(Also, what is its real name? I assume they don't call it a "space-modesty thing".)