Passport has to be submitted, typically, within 30 days. Takes them about 30 days after that to get it back with the COPR and visa attached - which is the paperwork your wife will need to take with her to a Canada port-of-entry to "land". The COPR and visa have an expiry date on them that coincides with the expiration date of her passport, or the one year anniversary of the immigration medical exam, whichever comes first. She MUST land before the expiry date of the COPR. So, it's possible to estimate what the landing date needs to be if she can remember when her immigration medical exam was conducted.
If it's soon and she is not certain the child will be well enough to be left, she can fax a request to Buffalo with Drs letter/confimation explaining the situation and ask to delay submission of the passport. I don't think this would be an issue. It may end up that she is required to obtain a new medical exam - because there has to be validity to the medical results in order for them to issue the COPR, but if she tells them about her daughter, that she is aware that her medical expires at such-and-such time, and that she would be willing to redo the medical in order to extend the validity of the COPR issuance - BEFORE they issue the COPR - it's possible they would just put things on hold until her daughter is better. Possibly more effective is for you to try to get your Member of Parliament to make an inquiry of Buffalo for you, considering the circumstances - especially if time is short. They usually have contacts at the office of the Minister of CIC, and they can talk to someone in Buffalo directly to get answers.
The difficulty is trying to get Buffalo to respond to "outside" correspondence. You could sit on pins and needles waiting not only to find out whether they agree, but waiting to find out if they even got your original request. Better, if at all possible, to comply with what they ask - if it turns out there are several months until the medical expires, and she has some time. If not, she's either going to have to try to get a response from them, or do the landing and then return home immediately after.