Yes, it is. Spoken with an accent it could even be puzzling. A mother is "with child" if she is pregnant. A mother is "with her child" if they are simply together--a mother pushing a baby in a stroller is "with her child." Hearing "with child," I would wonder "did the speaker really mean 'pregnant,' or did she mean to say ''with her child?'" In the United States, if a woman is pregnant, and has said so to everybody--then we would say "she is pregnant" or "she is expecting." If a woman has not told people that she is pregnant, then it would be impolite to discuss it openly. Fifty or a hundred years ago, the word "pregnant" was not polite and you will read various euphemisms in older books.

Yes it is! People will understand what you mean when you say this but it is an older expression.

Yeah, that is super-old, so old it's archaic. Although everyone would understand it, no one would use it. It sounds like it's right out of the King James Version of the Bible.

Yes, it is quite an old-fashioned one. But, it is still used.