What I have learned, since having a 2nd child is... to regard my Eldest child, as a child, per her age.
Not only as a 'Big Sister."
Sometimes, young children can get real stressed, by always being told they are a "Big Sister" all the time.
Nor do they automatically know how to be, a "big sister" by default.
My eldest, my Daughter, would actually tell me "MOMMY, I am just a little kid! Not a grown up!" when she was stressed or felt inside herself... that too much pressure.
Many times, an Eldest child is suddenly thrust into an "older" role, but they are not, older. They are still just the same age they are and still a young child too.
Just because a child has a sibling and they are the Eldest, does not mean... that they are suddenly by default, 'older.'
No matter what, we go according to our kids cues and ages, per 'expectations.' Not it being based on who is "eldest" or who is "youngest." And not expecting behavior or the child's needs, to be according to their birth sequence.
My Daughter is 8 now. She is a real good "big" sister. But I can tell, when she feels just overwhelmed. She will just, need to be a 'kid' herself. And just need me... and bond with me... and have a relationship with me. Not it being just based on how much "time" is spent with a child or how one is keeping a child 'busy.'
It is about 'bonding' with and having a 'relationship' with your Eldest. Too.
My daughter, will tell me "Mommy I am just a kid! I can't be perfect all the time!" when she is feeling the 'pressure' of being an 'eldest' child. Even though, we do not put pressure on her or have separate expectations on her, just by sibling sequence.
She is still, at 8 years old, just a kid, too.
My kids are very close with each other. Very bonded. But even they have their moments.
You also need to explain to the Eldest, about baby development... how to be gentle, how a baby is not a toy etc. That is what I did with my daughter. She was the same age as your Daughter... and she really understood. It helped her that I explained things to her. A child does not automatically know... how to handle a baby, on their own. They have to be taught.