I'm content that I can finally pick up my bull (even when conscious) and drop him in a bed (he actually just stands there, but it says he's sleeping). Not being able to heal him was a pain because.... he's a big hitter, and those charges can be so dangerous when he catches more than one enemy. I think I've only managed to survive because of him.
Still prefer an actual pet bed though, maybe a sty (pigsty) where your pet can rest, or you could drop an unconscious stranger in it to recover faster (when you don't want this stranger in your house).
It'd also be cool if the pet could idle in the sty and thus conserve some food while they are waiting for something to happen. Idle like humans do on pillows (instead of beds, but either way would make me happy).... I should probably post these feature requests in requests soon.