I translated the sentence this way too. Probably because of all the priming in the previous section with the expression for watching tv. Do you know if watching to seeing is more appropriate in this instance?
The verb to see is not usually used like this (is seeing) but to keep the literal translation in duo I think you have to use the verb 'to see'. In English we would probably use a different verb in this tense 'to look' which would transalte as 'The dog is looking at itself'