Harry Ricketts' biography gives details of the event. The opening pronoun here refers to Alice and Lockwood Kipling, Rudyard's parents.
Their son was born at ten o'clock on the evening of 30 December 1865, after six days of labour—"as long as it took for the creation of the world," as Alice later quipped. The servants sacrificed a goat to assist a safe delivery and quick recovery. [Ricketts op. cit., page 7.]Six days! That would get you a handsome medical-malpractice settlement nowadays, though perhaps not in India.
I reviewed Ricketts' Kipling biography, along with Andrew Lycett's and some related books, for The New Criterion back in 2000.
That review—it is really an extended essay on Kipling—turned out to belong to a genre dear to the hearts of us poor Grub Street hacks: the genre of literary productions that yield a trickle of revenue for ever after via reprint requests. I must have made a couple of thou from it altogether these past 15 years.
I reviewed a different book about Kipling here.
And speaking of The New Criterion: the forthcoming (January 2016) issue carries my review of Matt Ridley's new book The Evolution of Everything: How New Ideas Emerge. My review has a scathing (I hope) on-topic (for VDARE.com, that is) flourish at the very end.