For a highly intelligent person, especially a child ahead of her peers in school, I find that the best remedy is reading. My wife is a teacher and swears by phonics. She taught all my children to read early, and to this day that has served them extremely well. My first is now in college, and loving it. My second is a junior in HS, but already being recruited by top universities like MIT, Harvard, Caltech and others. When school gets boring, they pick up a book and read. Sometimes it is fiction, but sometimes it is a biography or a science book. My son has often picked up an Encyclopedia (yes, old school, hard-bound World Book Encyclopedia) and read through several articles in a sitting.
I would strongly suggest that you learn about phonics and take your child through it. You can start by putting up an alphabet chart or just the alphabet letters all in a row, big ones, all around her room. Then each day teach her one, its name, and its sound. My wife did this with my son, one letter per day, but when she got to M, my son got impatient and made her sit down and teach him the rest of the alphabet in one seating.
Read a lot with her, and point to the words as you are reading them to her, and don't limit yourself to books for just her age. I read the Chronicles of Narnia to our kids several times, before they could read, substituting their names for the names of the kids in the book, and they loved it.
Teaching a kid to read and to love reading is one of the best gifts a parent can give their child. For a gifted child it is even more special as it gives them a way to feed and exercise their intellect that is only limited by the size of the libraries available to them.