There are things found in water that can make any animal sick. Medications, protozoa and bacteria can all do it. (Typhoid, Cholera, Giardia, Dysentery, E. coli).
However, unless someone who has these diseases is spitting, peeing, pooping or washing their hands in your tank, it's unlikely they will be in the aquarium.
Heavy metals, herbicide, pesticide, fertiliser will all make dogs sick if they drink contaminated water but they usually kill any fish, shrimp and snails in the water.
If you do big regular water changes, gravel clean the substrate and have a clean filter, there shouldn't be anything major in the water that is going to cause problems.
This doesn't mean that aquarium water is safe to drink. Some animals have sensitive stomachs and might get sick from drinking aquarium water. But it is more likely to be from another source, and not from the aquarium.
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See if you can find out what the dog has been eating. Dogs can eat most foods that humans eat but some foods we eat can kill dogs. I used to feed my dogs the same food I ate (meat & veges) and they never had a problem. However, some dogs have food allergies/ intolerances just like people do.
If the dog has been bitten by ticks, it might have MMA (mammal meat allergy). Dogs with this issue cannot tolerate red meat and have to be fed on chicken or fish so they don't get sick.
Most dogs are lactose intolerant and can't tolerate cows milk. Does anyone give the dog milk or dairy products?
Foods that dogs should not eat include: grapes (including sultanas & raisins), onions and onion relatives (garlic, spring onion, shallots, leeks), chocolate, coffee, paracetamol or aspirin, cashews, macadamia nuts, avocado, artificial sweeteners like xylitol, and mushrooms.
There are also plenty of plants that make dogs sick including: ferns, palms, lavender, aloe vera.
There might be things around the house the dog is eating or chewing on that could make it sick. Does anyone use bug sprays or use roach baits, ant powder, etc, around the property?
Hairsprays, perfumes, deodorants, paints, cigarettes, hand sanitiser, etc are all poisonous to dogs and if the animal licks or eats it, then the dog might get sick.