The use of the present perfect and past perfect does not correspond with specific time references, like "today" and "last week". The rules on their usage are different. I recommend that you study these grammar topics more.

Possibly "I hadn't washed the dog in the last week, so I washed the dog today." ----------------- * when you say "a dog" it makes it sound like you're walking up and down your neighborhood, finding a dog, washing it, and then setting it free. Then a few days later, you find another dog and give it a bath. Maybe that is what you mean. But chances are, you are washing a specific dog. So you will want to say "the dog" or "my dog" (if it is yours).

I had washed a dog last week and I had washed a dog today.

I think you're trying to say: I washed my dog last week (or a week ago), so I have to wash him/her today.