In th English translation of The Kindly Ones, a 2006 novel by Jonathan Littell set during World War II and its aftermath, the narrator states: the source
I picked a woman from a good family; she was relatively good-looking, a proper sort of woman, and I immediately got her with child, to keep her busy.
I have two questions according to the text:
Correct, "got her with child" means "got her pregnant", because "with child" is an old-fashioned idiom meaning "pregnant".
"Got her with a child" would not have as clear a meaning and would be liable to be understood differently: outside of idioms and without clarifying language or context, the word "child" usually refers to a child who has already been born.
From Oxford Dictionaries Online:
with child
archaic Pregnant.
‘Yesterday, I drove out to St. Thomas to do a little private practice for one of my colleagues who is with child.’
‘The duke had no heirs, only a wife who was about five months with child.’
‘Not being with child, I cannot attest to the truthfulness of the latter claim - and there is only so much I'll do in the name of research.’
‘While I walk, I muse on art and life. Back home, I make breakfast for Rose, who is with child.’
‘Slowly, her body returns to the form it was before she was with child.’
with child refers to the state we call "pregnant".
"to get someone|something {state-phrase}" means to cause it|them to be in {state}.
The sudden downpour got him wet.
Stepping into the puddle got his shoes wet.
The real estate agent got the house sold quite quickly.
The duke got the duchess with child.
It's also worth pointing out that this is an archaic usage. No one would say "I got her with child" today, you would sound very silly; "I got her pregnant" is the modern usage. It's perfectly appropriate, however, for a historical novel, or for dramatic effect in fiction.
