Could this also mean "Where are you running from?" or "Whence are you running?"
It could be used in that way. If you expect an answer like, "the castle" or "the neighboring kingdom" or "my home", then it could be interpreted that way. However, the more common way to say that would be using nuqDaqvo'. I know it looks like I've used conflicting suffixes, but nuqDaq has become fossilized and can act that way. Most likely nuqDaq is not actually nuq with the suffix -Daq, but rather probably the question word nuq smashed together with the noun Daq ("location"). But that is purely speculation - we don't know the true etymology. So, in this course, because the answer could also be "from the guards" or "from the explosion" or "from a flood" we will only accept "what", and not "from where" or "whence", as translations of this particular sentence.
nuqDaqvo', or any kind of suffix on nuqDaq is not attested in canon. It cannot be said to be more common.
Using nuq to refer to a place is not unprecedented in Klingon: http://klingonska.org/canon/1999-07-19c-email.txt . This is a slightly different case, but Okrand there points out that using a what question where English speakers expect a where question can happen in these cases.
But without evidence either way, I would avoid translating nuqvo' as whence, and I would avoid using the word nuqDaqvo', whose validity is uncertain. Do what Okrand did in that message and side-step the issue. Use something like Daqvo' SuqettaH; Daqvetlh yIngu'! You are running from a place. Identify that place!
It is an interesting feature, but something I would definitely see as an aesthetic flaw in any language that was trying to look like a natural language. I cannot think of a language that requires such an elaborate periphrasis for a question that surely could not be any more uncommon in Klingon than it is in any Terran language. It is a minor flaw in a lovely construct, though, and I see myself more an appreciator of Klingon than a speaker of it, so I probably won't worry about expressing this in any case.
It's commonly known as the "ship in which I fled" problem. You could say "identify the place from which you come," except you can only construct relative clauses where the head noun is either subject or object of the clause.