if you can spend some quality time with your eldest – just one on one – letting her know how wonderful you think she is – that might help. Also say nice things about the eldest when she is being good (or at least not harmful) and she is around the youngest. I’m not suggesting you don’t do show your love already but it really sounds like jealousy – which is normal.
My daughter did this with her baby sister and I’m pretty sure it was jealousy. I used to just tell her that was naughty behaviour, and she needs to say sorry and give her sister a cuddle cause baby sister is sad now. She doesn’t do it anymore, it’s normal and it will pass 🙂
Generally you will find if a child is hurting others they are hurting in some way themselves. It sounds like she desires your attention.
read a great article on this – we have had similar problem but in reverse (toddler hits 4 yo). The article explains why timeouts don’t work and has a great suggested conversation which I find really helpful – a ‘script’ to work from. http://www.ahaparenting.com/_blog/Parenting_Blog/post/The_Best_Way_to_Stop_Sibling_Violence/
In my opinion it sounds like she’s after your attention. Try and give her positive attention instead – time in rather than time out. Of course hitting isn’t ok, but before she gets to hitting maybe ensure she’s getting enough of your positive attention. Praising when she plays nicely etc. You could also try not giving her attention when she does hit, by removing your 1 year old and making a fuss of them, rather than your 3 year old.
Alternatively, it could be frustration and she doesn’t have the words to tell you how she’s feeling. I’ve taught my 3 yo to ask me to move her baby sister away if she doesn’t want her to play. I always respond but sometimes I don’t move my youngest, instead suggest a way they could both play, other times I move her. This seems to be working for us at the moment.