Grammatically, it is correct, since word order typically does not matter in Latin. However, their could be multiple ways to rearrange the sentence which may be difficult for the creator/computer to have as correct. But, your translation still works, just not the way they want it.

This was frustrating for me. It is actually a big problem in the program's ability to teach Latin. Because Latin is a synthetic language that uses inflection as its primary syntax, the endings of the words--not their order-- are simply how meaning is made within the language. Latin word order, as written by Romans, is often very different from the word order we are accustomed to in many modern languages, so counting something as wrong because it doesn't fit Duolingo's exact, restrictive word-order template seriously misrepresents the language. Romans constantly played with word order to convey stylistic nuance in their sentences. I am a Latin teacher myself, and "Frater scribit domi" is a perfectly correct way of writing that sentence. Duolingo is just wrong on this one. I realize that it's in Beta at this point, but if they can't figure out how to fix this part of their programming, it will be virtually worthless as a tool for learning Latin. Perhaps this is part of the reason why google translate is so bad with Latin? I don't know enough about computer programming to be able to tell if the syntax required for computer programming just isn't sufficient for dealing with a synthetic, inflected language like Latin, but it seems like this may be part of the issue. I can't imagine how difficult it would be to program a computer to be able to catch meaning the way it is made in Latin (and other ancient languages like it). There's a reason why many of the modern versions of these ancient languages dropped inflection in favor of prepositions and word order . . . they're easier to speak conversationally that way. I suppose that's good for me, though--maybe we will always need non-virtual teachers of Latin!

"Domi" is locative/adverbial, so it doesn't need a preposition.

"Domus," along with other words (cities, towns, "rus"), actually have a Locative case; here, domi. Further, in scenarios where "in" is equivalent to "in" (without motion), the noun would take the ablative case "domo," not the genitive/locative "domi."