I really wouldn't worry about formal seat work for a 3yo at all. She is learning all the time without you making her sit down. Making her do this will eventually make her dislike learning. You want her to have a love of learning. She's just a baby...well, you know what I mean. She's got plenty of time to learn how to write. I know we all want our children to be the smartest, brightest, earliest writing and reading child, BUT we have to be realistic too. Don't force her...she'll be asking you in no time what this and that is, etc., and then you'll be the one struggling to give her all the information she is wanting.
My 4th child is 3.5yo..she's a girl too...she came to me a while back asking me questions left and right...she wanted to know. Oh, one thing I did with my 2 oldest boys (10 and 11) when they were younger was do musical chairs with paper plates and written on those paper plates were the letters of the alphabet...except I had them tell me the sounds they made...that was about 4yo. It wasn't a normal musical chairs game of course, but they had loads of fun. Another great thing is getting a salt box.....a box that is fairly low..maybe a shoe box...and teaching her how to write her letters in that with her finger. Those things are fun for most kids. I would just let her be 3yo.
My oldest when he was 3.5yo went through a Kindergarten math book in about 5 months. Then he moved on to a 1st grade book, etc. He was learning his sounds and writing at 4yo. His brother (just a year younger) was NOT ready for that until 6yo. He wasn't ready to write, to sound out any letters, etc. He did however begin math early similar to his brother...about 4yo, and not that quick. My 4th child, our girl loves to learn, asks us to read to her all the time, asks this and that, and this and that. Our 5th child is only an infant...another boy...we'll see how this goes with him. Each child is different. My .02 worth.