Dogs can have catnip. It will not make them sprint around the room. In dogs the same plant tends to act as a mild sedative, which is the opposite of the cat's ten-minute burst, and it is easy to oversell that as a fireworks cure.
It is non-toxic. A small pinch is the dose. A raid on the cat's stash is how you get an evening of wind and, sometimes, vomit.
Why dogs do not get the zoomies
Nepetalactone, the oil that about two in three cats respond to through smell, does not hit a dog the same way. Dogs that notice it at all usually get quieter: a bit sleepy, a bit less tense. Some dogs notice nothing. There is no equivalent of the inherited "catnip gene" conversation, just a plant that may or may not take the edge off.
People also use it for a mildly unsettled stomach, the way you might use a mint. That is traditional rather than veterinary advice. It is not a replacement for a travel tablet your vet has already recommended.
Is it bad for them?
Not in household amounts. It is a mint, it is not poisonous to dogs, and a curious dog that licks a catnip toy is not an emergency.
Too much dried herb, like too much of any fibrous plant, can mean vomiting or diarrhoea. Take it away, offer water, and wait. If that continues, treat it as any other dietary upset and call the vet.
Constant access also means the effect, if there was one, fades. A pinch on a noisy evening is a different proposition from catnip in the food bowl every day.
If you want to try it
Start smaller than you think. Roughly 1/8 to 1/2 teaspoon of dried leaf on food is the usual range, depending on the size of the dog. A few fresh leaves, chopped, if you grow it. Wait and watch. Some dogs will eat it and go to sleep. Some will ignore it.
Giving it about half an hour before a known stressor — a storm, a short car ride — is the only timing that makes sense, and even then it is a mild herb, not a sedative drug. If your dog panics at fireworks, talk to the vet rather than scaling up the mint.
Do not add it to the water bowl as a standing arrangement. You cannot control the dose, and stale herb in water is an unpleasant drink.
In a house that also has a cat
Keep the cat's toy out of the dog's reach if the dog is a chewer. A cotton toy full of herb is interesting to a dog as an object to destroy, and you will be left with a ripped seam and a pile of leaf. The toy is sized and filled for a cat; it is not a dog chew.
Offer the dog its own pinch, separately, if you are going to offer it at all. Sharing the cat's session usually means the dog eats the fill and the cat loses the toy.