E.A.
"Officially" plan your daughter's party for a few weeks after your baby is born, send them invites, etc. Tell them you are planning something AFTER your daughter's actual bday because you're not going to be feeling up to it during her actual birthday. I am 39 weeks pregnant right now and know exactly what you will be feeling. I agree with the other response, though, that you need to just be honest about the situation. GOOD LUCK!