You’re absolutely right that this is not an uncommon problem. Jealousy between siblings is extremely common to the point that it’s a normal issue that every parent faces, not just once but on many occasions. Even if you had been writing about an oldest child, there would be no reason to dismiss your question as the “normal anxieties of new parents” who have yet to see children growing out of issues. Jealousy is something that we can find almost everywhere we look, and it’s understandable that it concerns you and that you want to help your daughter deal with it.
It’s refreshing that you describe your daughter as a gentle child, and that you see her positive qualities even though you’re looking for advice regarding the difficult aspects of her personality. It’s a shame when someone’s challenges overshadow more pleasant aspects of their nature.
That said, in this one area where she is expressing her jealous feelings, she is not so much being gentle as quite stubborn and inflexible, insisting that she absolutely will not be able to handle getting anything less than her sister, even though it’s the sister’s birthday and not hers. Hopefully, addressing this now, while she’s still young, will help in preventing her from growing up into a child who is gentle and obedient as long as she gets her way, and stubborn and even manipulative when she doesn’t.