I definitely have an independent child. Yes, she taught herself to read at 2, her first sentence was "I DO IT!" (stated emphatically with tiny hands on hips and a foot stomp for good measure) and she also "just decided" one day to use the potty at not quite 1 1/2.
Here's how THAT story goes. Because she was already "ahead" of the other children, the daycare asked to move her up with the two-year-olds (something that generally didn't happen until 2 1/2). At first I said no, because I truly believe children should be with their own peer group. But, after much discussion and a couple of trial days in the two-year-old class I finally agreed.
When I picked her up after her first full day the teacher said to me, "I didn't know Janan was potty trained! How wonderful!" I thought for sure she had confused my daughter with someone else so I said, "THAT'S my daughter (pointing to the child she apparently didn't know was mine.) She's not potty trained, yet! I don't think she's ready." The teacher then gave me the oddest look and said, "Well, she's been using the potty all day!"
Truly thinking this woman had lost her mind, I knelt down and said to Janan, "Honey, did you go potty in the big potty?" and, as is typical with this amazing child of mine, she simply looked at me and said, "Gaby-elle go pee pee in the potty, Nee-Nee go pee pee in the potty!" (Gaby-elle was actually a little three-year-old girl named Gabrielle getting ready to move up to the next class and she & Janan - she called herself Nee-Nee at the time - had apparently become fast friends). From that day forward, she only used the potty.
Needless to say, she LOVES reading about children (especially girls) who are very independent. What little girl could be more independent than Pippi Longstocking? Designated for children 9-12 years of age, Janan began reading Pippi around age 6. She loved the fact that Pippi had no parents, a monkey and her very own horse living on her front porch.
Pippi also has a delightful way of taking any seemingly bad situation and turning it into a true adventure. She's convinced her father, blown overboard during a storm at sea, is living on a island with cannibals and as soon as he can build a boat will come and make her the princess of the cannibals.
What Mama loved best about Pippi is her ever generous spirit and gregarious nature. Sadly, many of the independent girls in books are brash, bratty and rude (e.g. Junie B. Jones - yes, Janan read every one of those books, but Mama was never a big fan; and, yes, I know how unpopular it is to say that.). Now, Pippi definitely has her faults! She's known for stretching the truth a bit (OK, a LOT) and she's quite mischievous, but she's not purposefully mean-spirited or rude.
Also, because these books were written originally in the 1950's there are some things that had to be discussed while Janan was reading these books. At the very beginning one of the gifts Pippi gives her friend Tommy is a "dagger with a shimmering mother-of-pearl handle" and at the end of the book Pippi finds, among other things, "...three pistols and a sword" in a chest in the attic and fires off the guns.
As with any book, I think it's important to keep the communication open. Ask about what they're reading! Not only can it create some great conversation, but it gives you a chance to clarify when something like children firing guns comes up.