"Dat doet jullie hond altijd!"
Translation:That is what your dog always does!
You could alternatively translate "Dat doet jullie hond altijd!" with "Your dog always does that!" In that case, there is no "what", just like in the Dutch sentence.
However, if you want to put the "that" at the beginning of the sentence in English, you use "what" (doesn't make sense without it - "That your dog always does!" or "That does your dog always."). You simply don't need to use anything like "what" in the Dutch sentence.