Goodness girl! Take it back a bit. There is absolutely NO RUSH to have your baby knowing all the academic stuff at 2! I have four kids and they all have an aptitude for different things and have different learning curves although all incredibly smart, e.g.:
Oldest boy - could speak full sentences at 1, recognized all his letters and some sight words by 1 1/2, had a very large vocabulary and clear pronunciation by 2 but couldn't care less about numbers and didn't do well socially at all! Today he is 11, incredibly creative and gets all As and Bs in school and a great illustrator and writer.
Next boy - couldn't understand a word he said until 2 1/2 and didn't even put sentences together until nearly 3, just wouldn't speak. He is going into kindergarten on one week and does not know all of his letters but can add 3-digit numbers together in his head. He is 5 and never stops talking now. Has amazingly creative ideas and can't get enough of numbers.
Next Girl - Is 3 and will not pee in a toilet (brothers both did it when they turned 2). She knows the alphabet and counting (most by sight as well) but cannot draw a thing (both brothers show an aptitude for drawing). She cannot copy anything but a circle. Loves to draw and read books and has a HUGE tude! We are not sure if we are going to make it through 3 with her. Ha ha!
Baby - Yet to see where she is, maybe a culmination of the three others.
Basically what it comes down to, all kids learn and do things at different paces. In our society we put a lot of focus on what our kids can do and how soon, when in reality the kids that do the best in school are the ones who "learn to learn" a not what they learn.
In other words, at two if you start creating habits that are fun with learning and read every day together and all she does is look at pics, your little baby will be the one that excels in school. She will be the one that has the vigor to learn because that is what you taught her. Don't worry about the technicalities, she will have her day when the letters and numbers mean something to her, just help her enjoy the process. You also need to really take notice on her ability to tell stories like she does, what a gift. This leads to so many incredible abilities in life, i.e., creative writing, logic, attention to detail, etc. All traits most of the population does not have.
If you want to play letters an numbers with her, try getting those foam bathtub letters that stick to the side of the bath. Every time she takes a bath just play with them with her. For a long time all my kids did was make boats, pictures and everything else with them, but every time they touch one I say what the letter is. It is totally fun. You can also count every time you put food on the plate or put socks on, so it is not a chore, just something you do. She will start to see the significance and start counting with you. Totally fun, no stress, no pressure.
Good luck