ECO modern essentials has a collection of oils especially designed for little ones. As for pets, especially cats, using a vaporiser is never safe as it spreads oil particles in the air that can stick to your pets hair which they will later lick off. Cats don’t have the liver enzymes to eliminate toxins in their body so can get very sick. If you are going to use a vaporiser you need to make sure your cat doesn’t have access to the room you are using it in.

I know a child who was rushed to hospital with severe croup. They used vicks / eucalyptus oil and discovered he was allergic to it (it made him worse). I don’t remember what they switched to.

The chemist warehouse oils seem good. Otherwise doterra has easy air which is a blend that works like vicks and on guard which is another blend made for fighting off germs and stuff

It’s recommended to use essential oils that are specially made for baby cold/flu just to be safe. So you could check out the Vicks range, oil garden, Euky bear at chemist warehouse. I would probably go with Vicks if I didn’t have much time to research.