There are a couple of UI indicators that your pet is dead:
-Special skill is grayed out (not too noticeable)
-Health bar is darkened (and not going down, relatively noticeable)
These along with the other signs:
-They aren’t attacking (duh)
-Pressing the skill button does nothing
-Your character almost always says something when they die
Means it’s not all that hard to tell. I agree though a stronger indicator would be a simple and effective improvement.
I probably pay way too much attention to what my pet is doing though. Some people in dungeons have even argued with me to leave them passive, even though it’s as simple as hitting F3 if you want them to not go ahead. I suppose it also helps that I have these commands easily accessible on my mouse so that I can use them while moving and doing other things.