You're kinda asking two questions. One is in your title: could other worlds have a different plan? The other is in the question: was there an option for our world?
The answer to the second question is "no," as was explained by @Tom.
The best answer we can give you to the first question is, "apparently." Please keep in mind that the answer doesn't matter — the rules for us apply to us and whether or not they apply to anyone else doesn't matter at all. Conversely, the rules for others apply to others and don't apply to us at all. Knowing that, we have two evidences that suggest other Plans of Salvation could be different. The first comes from scripture:
All truth is independent in that sphere in which God has placed it, to act for itself, as all intelligence also; otherwise there is no existence. (D&C 93:30)
The second comes from our Temple services. Please forgive me for not quoting the service, we believe it to be our most sacred, but what it teaches is that when Satan tempted Eve, he was acting in a way he had known used on other worlds.
So, does what I said prove a belief that other worlds may and/or do have other plans? No, it actually doesn't. It only suggests a possibility.1 And officially, the Church has no doctrinal or dogmatic statement on the subject because, as I said earlier, it doesn't actually matter.
1 The two sources I cite and verses from the Books of Abraham and Moses have been used by some over the decades to speculate a great many things. Perhaps the most peculiar is that Jesus died for people on other worlds. But they have also used these verses to speculate both that other worlds had the same Plan and other worlds had different Plans. It's all speculation — and considering how precious little the Lord has revealed about what may or may not go on with other creations of our Heavenly Father, it's wild-and-crazy speculation indeed. It should go without saying that absolutely none of it represents Church doctrine or dogma.