Equipment, weapons, and armor are generally protected when a character is hit by some kind of AoE. RAW, every creature in an AoE would make a save or suffer bad things.

If a character were carrying a puppy or if they had a puppy in their backpack, would you rule that the puppy dies if the party gets hit by a fireball?

Creatures are not considered items (this remains true of items that turn into creatures: they are a creature when they are made to be one). So, regardless of whether it is being carried or not if in the Spell AoE then it suffers the damage.

However,  Spell AoEs do not go beyond total cover, and for "reasons" (aka designer laziness) cannot affect objects unless specifically stated so (regardless of how incredibly unrealistic that is) so if a creature was in a bag fully contained with total cover it remains safe from the Spell AoE.

Quote from Brian_Avery >>

...so does that mean the puppy is 100% safe (is there an echo in here lol)

YAY! We can all enjoy Christmas.

 
If it was just on your back, no it gets blasted (that's half or 3/4 cover depending on size, most AoEs can go round corners). If it was fully enclosed by an item like a backpack then it is 100% safe.

To be honest if this was a pet then as a DM I'd just use DM shenanigans to ensure it's safe anyway. Within reason. Because, ya know, it's a puppy/pet. It's like how <Critical Role Spoile>

Yes, if it just a random feelgood pet/companion then it is safe. You would only put such a creature at risk of harm in order to advance the story not due to accidental fireball exposure (as you sneak across the ice bridge to safety you all realise, to your horror, that Jub-jub the puppy is still trapped in the frost cage - and the young blue dragon is about to wake up!) If, however, the party is on a quest to protect the cosmic puppy and get it to its interdimensional kennel to avert some cataclysmic event, then perhaps you might explain that the party must put more effort into its protection than "I shove the dog in a sack"...

Wow, I feel like such an evil DM, but I'd call the puppy dead if he's in range of said spells. Similar to mounts that are in range of a breath weapon of a dragon. That'll teach the characters to bring such helpless creatures into the adventuring life. :P

For real though, it makes no sense to me that a thin sheet of leather would keep a creature safe. And on that matter; I don't think an adventurers backpack is a suitable place for puppies/bunnies/tiny helpless critters. I mean, it's dark, it's cramped, there's a good chance there are solid objects contained within such as potion bottles or acid flasks. It might go for your rations (dried jerky anyone?) or rip your precious Noble's Clothes or worse; starts playing with your bag of holding and with its incredibly sharp puppy-fangs might rip it.

That said, it all depends on how gritty and/or realistic you want to make your game. Some DMs would have you maintain your weapons/armour/clothes, some negate that. Some use the optional rules for permanent injuries, some don't. If the party were to bring a creature along (ANY creature) I treat it as something the enemies might go for, increasing the suspense and make the players question the risk they are willing to take to keep said creature safe.

This is a bit interesting because if it's a normal backpack, items usually stay safe from a fireball as no one really deals with item loss like that from what I've experienced. If that's the case let the puppy live. Otherwise you need to start destroying items as well to be fair and not come out as a monster puppy killer. Instead your the jerk who won't let your party have nice things. Let the puppy live, unless your doing some themed hardcore run.

My own take on this is that if a pet doesn't take part in combat, then it's just part of the background. Same thing for crew on the players' ship when they get attacked. Unless it specifically serves the story, the crew goes below deck or whatever and they ride out the attack. But if bob the quartermaster goes for the ballista on the deck, he's fair game. If the puppy in the backpack wants to take a turn of combat to bite the goblin, then he gets the fireball same as everyone else.

Given the choice, players will pretty much always take a pass from my experience.

Rule of Cool. If there's a story reason to kill the puppy, do it (you monster), but there is no mechanical need to kill non-combatant living creatures that are essentially items. If the puppy doesn't have a statblock, a spot in the initiative order, and the ability to make attacks of opportunity or "help" its master, its a "puppy" item in their inventory and not a creature that the combat rules are designed to apply to.

If the DM is going to kill my dog, he'd better be ready for me to go John Wick in response :)

Quote from Wysperra >>

Equipment, weapons, and armor are generally protected when a character is hit by some kind of AoE. RAW, every creature in an AoE would make a save or suffer bad things.

If a character were carrying a puppy or if they had a puppy in their backpack, would you rule that the puppy dies if the party gets hit by a fireball?

 Schrödinger's puppy?

I would always rule that the PC covers the puppy from harm (with their own body if need be), so the puppy is safe from harm as long as the PC remains alive.