What is the proper etiquette when inquiring if a woman is with child?
There is none.

I googled “when is it ok to ask a woman if she is pregnant” and came up with thousands of responses.
Here’s my favorite:

(I would add another woman after delivery because it takes about 6 weeks for your uterus to return to a non-protruding state.)
I saw a patient for her first OB appointment today. Her sister was with her, was not my patient, but looked to be pregnant too. My first thought was to comment about how cool it was for them to be pregnant at the same time … then I questioned myself. What if the sister wasn’t pregnant? What if she was (to put it nicely) apple shaped?
Women in their child bearing age often struggle with weight fluctuations. Fat or pregnant? Don’t ask. If a woman is in her pudgy phase, the last thing she wants to be asked is if she’s pregnant.
If you think someone is pregnant and you are extending a courtesy to her (giving up a subway seat, holding the elevator door), still extend that courtesy. If the woman is not pregnant, she will appreciate the gesture just as much, as long as it’s not accompanied by a “when are you due?” remark.

Being an obstetrician does not make it right for me to ask random women if they are pregnant. Being in line next to someone at the market doesn’t give you the right either.

I apologize for not having the link to the picture. I found it online couldn’t find the original source. Let me know if you know if so I can give credit!