As of Episode 4, no dogs are dead. There are three more episodes in the first season, and there will be a second season at some point. The dogs might die in the future; I'll try to edit this comment as the show goes along.
If I see someone punch those beautiful animals, I will jump through the screen and Chop their hand off!!! This may be a reason why i stop watching this show. It better not be bad!
The show has an open ending, all bets are still on the table, but it is definitely not an unhappy-endig.
Also, the show has been renewed for a 2nd season.