Not a bug. Dogmeat is your go-to partner if you want to be "the lone wanderer" in FO4. He's also the only partner not to criticize you over anything, can lug around 149.4 stones(?) and I find to be pretty good at pinning random ghouls. Also features kick ass neck biting animations on smaller animals. Essentially, the only reason you should be without a partner in FO4 is because you find they just get in the way of shooting things or moving, and Dogmeat does make an effort to move towards where you're looking.
Though it IS odd that Dogmeat getting struck won't contract the disease onto the player, but activating the protectron and having that get hit will. It's also possible it's just a low chance on Dogmeat because he's virtually impervious to everything the wasteland throws at him. Radiation pools ain't got nuthin' on this mutt. Either way, I went in without him while wearing power armor my first run. Power armor can let you take a hit and potentially avoid getting infected. It's a good idea to kill a few mole rats, check stats, then save if clean. Also, close every door behind you. Little bastards aren't smart enough to open doors, unlike Dogmeat...