Nonbite exposures rarely causes rabies
But as antirabies vaccine
rarely has any side effects and there are few cases of rabies reported after nonbite exposures, by comparing the risk and advantage factor it is better to immunise the child for rabies.
So I would suggest you to get your child vaccinated by antirabies vaccine. Yes it can be given now as the incubation period
for rabies varies from few days to months.