I know "eng" is a common abbreviation of English, but please don't use "jap." As an American (or at least someone living in America), I hope you understand how the historical use of that word has tainted it beyond redemption.
1. Japanese is highly contextual, so the situation will greatly affect how this is said. If you mean that she's planning to cook this (in this case, "this" is vague and without context) early in the morning:
お姉ちゃんが(これを)朝早く作る(つもりです)。
Older sister will/(is planning to) make (this thing by me/in my hand) early tomorrow morning.
1. If you leave a plate of cookies out, all you need is どうぞ. The context says everything except who made the cookies.