Well, if you haven't had the baby yet, I would add my .02. I think you should call the friend, even if you don't know her very well. She offered, I think most people wouldn't do that very lightly. If things don't go well and you are looking back on this time, you will think your reasons for not calling her are pretty insignificant, compared to what's at stake, while I would imagine you would be unlikely to regret if you do call her.
Thinking of you.