If I had to choose just one book -- I cheated and read several -- I think it would be this one: If Your Kid Eats This Book, Everything Will Still Be Okay: How to Know if Your Child's Injury or Illness Is Really an Emergency, by the paediatrician Lara Zibners.
Apart from a terrific title, the book has plenty going for it. Basically, Even if Your Kid Eats This Book is a detailed guide to everything you don't have to worry about. It has an orifice-by-orifice guide to detecting and removing Lego! A list of things under the sink that won't poison your kid! Sensible advice about how to get rid of dry skin! (Hot bath, then anything greasy from Crisco to Vaseline, then time).
And of course, there's also very clearly spelled-out, highly specific lists of what is worth calling your doctor or going to the emergency room for; along with details about why those things are scary and what the worst could be (it's usually not very bad).
There's nothing more soothing than a list of stuff you don't need to worry about. Yes, 12 Hours Sleep By 12 Weeks is more practical, but once the kid is sleeping OK, this one is indispensable.
I write books. My latest is a YA science fiction novel called Homeland (it's the sequel to Little Brother). More books: Rapture of the Nerds (a novel, with Charlie Stross); With a Little Help (short stories); and The Great Big Beautiful Tomorrow (novella and nonfic). I speak all over the place and I tweet and tumble, too.