Hon, I didn't want to study too when I was 3. LOL
Relax, I have a son who's an honor student and speaks 6 languages fluently and now in college... is this your first?
At that age, all my son wanted to do is play... however, when my son was in elementary school, the principal wanted to skip him two to three grades, because he is that smart... I only allowed 1 grade skip because of his emotional state... he may be "book smart", but emotionally, he's still young.
With that said, allow your baby to enjoy her childhood... don't fret about what she's not learning, she will learn them in time.
I'll give you a piece of my secret that I did with my son. Okay, when he was at that age, whenever we're driving down the store, I'd point "blue car". By saying that, he learned "a" color and "a" noun. See! Then I'd point at a "red ball", "a yellow house", "a red firetruck" then pretty soon, we were playing that game all the time. Then for the alphabet, I bought a cassette (cd was too new back then LOL) and it had children singing the alphabet and I'd play that tape at home, in the car, at grandma's house, and pretty soon, he was singing them. LOL for numbers, I'd sing songs like I have two hands and ten fingers and ten toes, then I'd count my son's fingers and toes, in the tune of happy birthday to you. HAHAHA! But he learned his numbers. Next thing I knew, he was counting Cheerios on the dining table and I'd praise him for knowing his numbers... then we'd do the "dance", when he'd done something good. We had this "chicken style" dance, you have to make one up for you & your daughter. The sillier, the better! LMAO! Kids love silliness and it's fun.
Don't sit your daughter down to study, make it fun... I'm a single mother and at one point, I had a full time job and going thru grad school and caring for my 4 year old baby... I know what it's like to be busy and stressed.
I hope I helped you a bit with some ideas. Good luck and let us know your progress.