Agression is the only thing that I really give the under 2 year old set a "time out" for. I am not okay with hitting, biting, etc and feel that it needs to be communicated immediately. They are removed from the other children, to a seat in the same room and told firmly "We do not (bite, hit, push). (Hitting, biting, etc) HURTS." Then they sit for a minute. I have had very good effectiveness so far. They are not shamed, screamed at, or given any attention whatsoever. They do realize very quickly, that it is not an effective way of communicating or getting attention!
Does it still happen once in a while? Yup, because they are still learning. But it seems to work for us.
And until she figures it out and you can "trust" that nothing is going to happen when you are more than an arms length away, I would absolutely keep her with you everywhere. Its not fair to the other kids if they feel afraid when she's around.
On that note, make sure none of the other little ones are bothering her and are just flying under your radar!! She may just be pushing/hitting/kicking BACK. Or if it's happened in the past, then she might be thinking "I'll get you, before you can get me." When my boys were growing up, I was constantly giving the oldest one trouble about being more caring/kind to his little brother. Only to watch a teeny bit closer and see that my not quite one year old was totally instigating! He would do things to get his brother going, and then wail when our oldest retaliated. Tricky boy.