J.,
My daughter was 21 months when her brother was born. She wasn't nearly as violent to her brother as your daughter is but she did act out a lot. (She never hurt Aaron by scratching but when he started crawling she would pull his hair every time she went past him. She also kicked a lot, not specifically at him but if he was in her range then watch out.)
Time outs do not really work well at this age as the child only has a limited ability to understand what they did wrong and even less of an ability to remember and even less of an ability to control their behavior. A behavior specialist can probably help but your insurance most likely will not cover it. It may cover a psych consult.
OK, here is what I did. I did the pillow thing - I made her kick the pillow or hit the pillow when she was angry. (Of course my daughter was a few months older and those months do make a lot of difference.)I also reprimanded her with the same thing "No! Bad! Hurt!" over and over again. When she got older (around 26 months) I would make her pat the baby and say "sorry". I would explain to her after the incident that she hurt the baby. I would spend time while Aaron was napping doing things with just her (not cleaning the house or getting work done). I would spend babysitting time out with just my daughter even if it was just grocery shopping. But the only real solution was a lot of love and a lot of attention and never leaving her alone with the baby - ever! I had to keep a constant eye on her always. I had to keep them separated even when we were playing together.
I can tell you that it is very difficult to discipline a child at this age. And yes, even though I do not believe in spanking I spanked her twice over this. Stupid move - it did NOTHING to change her behavior, it only reinforced her solution that violence is the way to handle your anger. So remain calm and keep them separated.
Also instead of letting her handle the baby, get her a baby doll that can be her baby. If she wants to handle the baby, show her what to do with her own baby. It doesn't even have to be a doll, a favorite stuffed animal works well. I bought a second hand doll changing station, stroller, car seat, etc. and let her play Mommy with her Cinderella doll. That helped a lot.
Finally it does pass. My children are now 3.5 and 1.5 and they play together pretty well. Aemilia is still a bit of a bully at times and Aaron is a bit of a crybaby at times but now I can let them work it out themsleves unless it is a dangerous situation.
Good luck.
A.