I do not know where I am going, is very similar to I do not know where to go.
Peter, the DL sentence and your proposed sentence are actually rather different.
In order to utter your sentence, one would have to be at the moment in the act of going, but uncertain where to. In contrast, the Dl sentence would be uttered by someone before they had started to go.
Furthermore, the Czech "jet" is clearly an infinitive meaning : to go". There is no "I am going" anywhere in the Czech sentence.
Depending on the exact context, there are occasions when they could be used interchangeably. But I should note I am thinking this is true particularly during an informal exchange between friends where the word "to" might be dropped. "I don't know where I'm going (to)."
I suppose my colleague refers to the difference between ...where to go = kam jít/jet vs ...where I am going (to) = kam jdu/jedu
Rereading t+n for movement might be helpful :)