I'm reading a Shin Chan strip and he and his friends are discussing who is going to take care of the stray dog they found. One by one he asks his friends, and they all say they can't. Then, he says (without looking at his last friend)
Then, his friend, who is next to him, says:
So, in the first sentences, I don't get the だまって (no idea what it is) or the 置いてきちゃお. I know 置く as an auxiliary verb to say you're doing something in preparation for something else, but I don't understand it in that context, with きちゃお after it's て form.
Would be very thankful if somebody could explain to me the use of each of those expressions in the sentence.
Here's a pic of the panel itself: