One of the few robot stories from the golden age that wasn't written by Asimov, this is Compassion Circuit by John Wyndham. Well, I think so, though the story differs in some respects from your description.
The woman is called Janet and she is in hospital due to some vaguely defined illness not to give birth. Janet has a phobia about robots, but after being looked after by robots in hospital she decides she needs one at home to look after her. Her husband orders the robot, which is designed to look like a housemaid, and Janet calls the robot Hester.
The ending is similar to your description but:
Janet has her head grafted onto a robot body
When Janet's husband sees this he flees in horror but stumbles and falls down the stairs and is badly injured. The story ends with Hester phoning the hospital and saying:
Emergency?" she asked, and gave the name and address. "Yes, at once," she told them. "There may not be a lot of time. Several compound fractures, and I think his back is broken, poor man... No. There appears to be no damage to his head... Yes, much better. He'd be crippled for life, even if he did get over it... Yes, better send the form of consent with the ambulance so that it can be signed at once... Oh, yes, that'll be quite all right. His wife will sign it."
As mentioned in a comment, the story is available in this copy of New Worlds no. 35 at archive.org. The story starts on page 32.
