That was a wyvern egg. Dragons ≠ wyverns. I'm not even sure if Nabateans can even lay eggs, since FE3H dragons contradict established FE lore on dragonkin (Manaketes). But since I'm not too fresh on that either, it doesn't matter, yay!
Anyway, I think it depends on whether Rhea's human form menstruates, no? Since that is basically just getting rid of unfertilized ova, plus some uteral lining. (So yes, eggs are chicken menstruation. Have a nice breakfast.) If there is some analogue between the dragon and the woman, I'd assume these processes to correspond.
Which makes one wonder how pregnancy works when switching forms. I don't think the egg would disappear and teleport the fetus back into the womb upon transformation. So it's probably some form of viviparity (aplacental or not). Which immediately reminds me of how some sharks are ovoviviparous (i.e. the young hatch inside the mother). And let's face it, having dragons be like sharks is just metal as fuck.
Also birds are dinosaurs.