I don't think the Church would deny baptism to the child. It would have to have Orthodox godparents, and it would be on them to raise this child Orthodox, if the parents failed.
Personally, I also wouldn't "wait" until the whole household is ready. Why wait?
I was a premature baby and therefore, was baptized on Day 3 of life. It was the best thing my mother ever did for me! (....and she's done many wonderful things for me.)