A.J.
Yes it is normal.
There are two schools of thought.
1) It's not nice to discipline kids this young so you should wait, ignore, use cushy time outs and words, etc. (If you choose this, no, it won't just magically "pass" it will get worse as she sees she's in charge.)
OR
2) The younger you discipline the faster they learn. A little firmness up front saves nightmares later.
We are of the latter school, and my 3 under 5 are awesomely well behaved thanks to discipline. Even my 21 year old ex terror who started angry aggression much younger and much WORSE than the older two is now very good and happy thanks to FIRM nipping. My husband travels all the time so all the "leave them home" or, "Just ignore it and let it pass (escalate)" was not an option for me. I'm so happy now we nipped the stuff and I'm accused of having "easy" kids, but we were very diligent and firm between the ages of 1 and 2, and it carried a bit into the 2's, but terrible twos can be prevented by diligent early discipline. If you want a great book, let me know.