heeler and tires

We have a Red Heeler, that gets worse about trying to grab a tires as we leave.. New tire on the little Tacoma pickup 6 months ago and now we have a slow leak on a couple of them, this AM one was almost flat. Ruined tires I guess! I check them out close, and every darn ones have what looks like really small puncture and some of those form a crack. Nothing on the inside sidewalls. Can this darn dog do this, they are just cheap 4 ply tires I know. I don't need 6 ply and those are all too nubby and noisey!.