Nice.
Also, the point of the movie was largely dealing with animal stereotypes (such as those seen in Disney or Warner Bros cartoons). So, if you can think of any animals normally associated with hospitals or animal rescue, you could add them and see what role they might fill.
Such as...
Saint Bernards who are often depicted rescuing people in the snow and carrying barrels of brandy to warm up the victim. That's actually a myth which TvTropes suggests was taken from a painting and later used in cartoons. It was more likely that the rescue dog was sent out to sniff out people lost in the snow while a handler followed them, possibly with a flask of alcohol they could offer the rescue victim. Alchohol apparently has a 'warming effect' the person feels, but it doesn't actually help them and is in fact quite dangerous.
Dalmations and fire fighting.
In fact, there could be alot of dogs (or wolves or canines, if human-domesticated animals don't exist) who worked in rescue operations in historical times in the Zootopia universe. We know predators originally hunted prey species and so they adapted better vision and sense of smell to track their prey... but once that chapter of history stopped and predators and prey worked together, I can imagine quite a few predators took on a more "protective" role with their prey allies.
Like sheep dogs who would watch over flocks of sheep and protect them from wolves or foxes and use their sense of smell to sniff out anyone who got lost. If we assume that modern predators eat things like fish, bugs, cheese, chickens, eggs, or tofu or something to get their protein then it could be that those original guard dogs protected sheep 'farmers' who in turn paid the dogs in food they caught or farmed. Those early dogs found it easier to sit around guarding prey and getting paid in eggs and stuff instead of running around hunting their fellow animals.
Actually, reminds me of the CGP Grey video about animal domestication
Sheep and dogs are both domesticated animals in part due to their family-oriented society. Each wolf pack has an Alpha Male and each flock of sheep has one too. Imagine if those early instances of predator-prey cooperation were the result of a wolf pack and sheep pack meeting eachother, duking it out, and suddenly the wolf pack had a very hard-headed and woolly Alpha Wolf... or the sheep had an unusually carnivorous Head Ram. Or they just recognized they both had nice family setups and "At least they aren't like those shifty foxes, or those flighty deer."
Whatever the case, the first predator-prey alliances were between canines and herd based prey species and it worked surprisingly well. Other species eventually started following suit, mostly with the canines chasing away rival predators and promising to not eat their fellow intelligent animal and over time other prey species and omnivores started joining the Flock.
So, the canines were pretty much the front lines of search and rescue operation, first responders, and guard duty with the prey species starting farms and possibly running hospitals or tending to the wounded the canines rescued. Over time, society advanced so that various other species started joining the first responders ranks (cats for climbing trees, bigger animals to provide muscle, etc) until the time of Zootopia where there is a wide variety of species working in law enforcement, even if they tend to go more for big and strong species over ones like rabbits or foxes.
Soo... yeah. Dalmatians and Saint Bernards seem like the sorts of animals you could see in rescue or firefighting teams along with any other sorts of canines. Although, since everyone's intelligent and they have advanced technology then their particular natural talents wouldn't be
quite as necessary as they once were and they could just as easily be on due to the stereotype that "dalmations make great firefighters" as opposed to actual talent by the person in question. Same with St. Bernards... particularly since "Brandy isn't something you should be feeding the rescue victim, Keith. Matter of fact, you shouldn't be carrying it at all."
Amusingly enough,
geese make good guard animals. They honk loudly if they spot intruders, they get along with chickens and other birds, and use their wings to viciously beat any intruders they spot. If the intelligent mammals of Zootopia use birds as domesticated animals, then geese would make a very good candidate for the first guard dogs to be used by... guard dogs.