The baby was a week overdue (it was expected to be born a week ago).
The Question is "Is a week ago" correct? Should it have been "a week before"?
The Paraphrase is not needed
If we did use the Paraphrase it should be (it was due the week before).
The word Expecting is used extensively to denote pregnancy however the baby is Due to be born is the correct term for the date when the pregnancy will be full term. This is a defined time much like a train arrival time. An expected time is speculative (indefinite).
The Over night train from London, Euston, due at 6.05 will be delayed. The expected arrival time is 6.40
There is also no need to repeat the use of Baby, we have already defined the subject we are talking about.
The baby was a week overdue (it was due "the" week before).
However why use the paraphrase it is only repeating the information already given. Paraphrasing is used to summarise important points, explanations etc. That is, they repeat (in your own words) the main points in long or complex texts.
The baby was a week overdue = (it [the baby] was due the week before)
So we do not need the Paraphrase as it does not meet the above criteria.
How to Paraphrase a Text Thought, Co
"Paraphrase passages that present important points, explanations, or arguments but that don't contain memorable or straightforward wording.
expect verb (THINK) Cambridge English Dictionary
to think or believe something will happen, or someone will arrive:
expect verb (BE PREGNANT) be expecting (a baby) to be pregnant:
due adjective (EXPECTED) Cambridge English Dictionary
expected to happen, arrive, etc. at a particular time:
What time is the next bus due?
Their first baby is due in January.
the determiner (PARTICULAR) used before nouns to refer to particular things or people that have already been talked about or are already known or that are in a situation where it is clear what is happening: