Hi A.,
My son is almost 20 months and he has just started to hit also. He throws fits too and we are working on both. Sometimes I feel like I don't know what I'm doing either, or if what I am doing is working. I definitely can recognize his behavior right before he is about to have a fit and I try to talk him out of it. Basically it all stems out of frustration and their inability to communicate with us. My son doesn't have many words yet, so when he starts acting like he's going to have a tantrum I verbalize his feelings for him. I feel kinda silly doing it but I think it works.
I basically just let him know it's okay to be: mad, sad, angry....but it's not okay to feel that way and hit something or someone (mostly me). I just talk to him and say something like " I know you're mad you can't go outside and play right now, but we can go after dinner...etc". It helps some.
Don't get me wrong, sometimes it doesn't help and I'll put him in his pack and play (the designated time-out zone) for a minute to let him cool down. He can throw his fit in there until he gets it all out. I do think your daughter is too young for timeout. Even my son at 18 months didn't quite realize what was going on at first, I think he understands a little better now.
Also, when I start to see my son get really excited and think he's going to start hitting or throwing things, I'll remind him to calm down and that there is no hitting, throwing we have to be gentle to our friends, cats, or whatever.
Good luck. I think it's mostly a phase, but if you let it slide it might stick around for good :)
Updated: Ooh and yes as someone mentioned try sign language. My son would always scream while I was getting him more food to eat and so I taught him to sign "more". He does it all the time now and it cut down on his screaming at the dinner table. I like the baby einstein videos and so does he. We are working on more signs, like "help" "mommy" "daddy" drink and eat, etc.