For one thing definitely get her started in activities like puzzles and activity books. This is great for quiet times (girls can usually adapt to this pretty easily). Structure your day, but don't forget to play. Media is a great tool, use it in moderation. Have her love learning. That's the key element here. You're not forcing her to level up, you're teaching her that learning is a part of life.
Mathematics: counting with tactile objects like large buttons. Very basic addition to start. Schoolhouse rock is fun for math as well. She doesn't need to multiply off the bat, she just needs to listen, dance and play.
Language arts: learning the alphabets, small words, and sentences. Basic picture books are great here. Something my mother did with me at a young age: she recorded herself reading books on tape, and played it back while I slept.
Social studies / science: museums and science centers. Zoo and aquarium trips. Remember: learning is best experienced through fun. (Schoolhouse Rock works here too!) Do basic science experiments at home (ice melting/freezing, mixing water with food coloring).
Music and the Arts: NEVER NEGLECT THESE. They are impertinent to anybody's learning and education, as they connect left and right brains. Increases activity and fun. Sing songs. Color and paint (great for increasing motor skills). Make collages and scrapbooks. This is good for tactile memory keeping. Toy instruments are good, even if your little girl doesn't necessarily show prowess in an instrument. Play dress up. Play with dolls or other toys. Play pretend. These are an equivalent of theater.
Etiquette and Home economics: Basic manners. If you're Christian, basic Bible stories -- actually these are good for any kind of moral types of stories. As for home economics, have her shadow a chore -- make her think she's helping! Also have her start understanding the concepts of money - give her a few dollars and have her "shop" for things. She'll learn basic adding and subtracting, teach her taxes - multiply total by 1.0(whatever your state tax percentage is). She can do this on a calculator. This is definitely more of rote learning, as she'll need to learn this for the rest of her life. Example: I learned a little bit about tithing and percentages this way. I didn't know decimal points, but I learned money values and moving a period one space to the left. Btw, if you don't tithe, consider it giving to someone in need. It's a good practice for community outreach.
