There are a few things that can jump species but usually it is the dog giving it to the baby. It is called Zoonosis
A zoonosis (pronounced /ˌzoʊ.əˈnoʊsɨs/) or zoonose is any infectious disease that can be transmitted (in some instances, by a vector) from non-human animals, both wild and domestic, to humans or from humans to non-human animals (the latter is sometimes called reverse zoonosis). Many serious diseases fall under this category.
It is rare and a baby giving something to a puppy is hard to believe, that guy had no clue what he was talking about.
here is a list of some zoonosis
Partial list of zoonoses
Avian influenza (bird flu)
Barmah Forest virus
Bolivian hemorrhagic fever
Borrelia (Lyme disease and others)
Borna virus infection
Creutzfeldt-Jakob disease (vCJD),
a transmissible spongiform encephalopathy (TSE)
from bovine spongiform encephalopathy (BSE) or "mad cow disease"
Crimean-Congo hemorrhagic fever
Cutaneous larva migrans
Escherichia coli O157:H7
Eastern equine encephalitis virus
Western equine encephalitis virus
Venezuelan equine encephalitis virus
Korean hemorrhagic fever
Kyasanur forest disease
Lymphocytic choriomeningitis virus
Mediterranean spotted fever
Ocular larva migrans
Omsk hemorrhagic fever
Orf (animal disease)
Psittacosis, or "parrot fever"
Rift Valley fever
Ringworms (Tinea canis)
Swine influenza (swine flu)
Tularemia, or "rabbit fever"
Typhus of Rickettsiae
Venezuelan hemorrhagic fever
Visceral larva migrans
West Nile virus
Other zoonoses might be:
SARS (possibly; civet cats may spread the disease, or may catch the disease from humans.)