Are they any diseases a cat can get from a person who was around other cats?

Sure there are. One that comes to mind right away is ringworm. It is a fungal infection that can jump for cat to person to cat or dog. She would have to touch the cat. Fleas, not exactly a disease but can bring them home from an infested place. Scabies, mange mites. The mites live in the hair follicle and cause intense itching, again, she would have to touch the animal. Depending on whether your daughter is a toddler or not, intestinal parasites. Toddlers are not known for having good hand washing protocol so it is easy for them to bring dirty hands with parasite ova to their mouth and ingest. Perhaps the feline virus, but not sure about that. This sounds like a good question for your vet.