Don't worry-- it's not bragging. It's information gathering. Your little one sounds like a real firecracker!
There is no such thing as "too young to read", provided that it is the child who is hungry to learn. My DS was an autodidactic reader before 2, as well. Would I have ever actively tried to teach him to read then? No. But some children don't wait for their parents to clue in!
My DS3.5 had similar interests around that time and loved to make up real and nonsense words with magnetic letters. We'd also borrow boatloads of books from the library, and I'd have him sound out words in the title, which are often printed in colorful, large fonts. Wordplay has always been a big hit, too.
